L-17 | Aptitude: LCM & HCF| NIPER JEE-2026 | Power Punch #niper2026 #aptitude #LCM #HCF

Indexed: 2026-05-21

[00:00:01]Hello students, welcome back to GDC. So today we have brought Nipper JE Power Punch in which we are going to talk about LCM and HCF.

[00:00:11]LCM and HCF is a very easy topic. LCM is our least common multiple. HCF is our highest common factor. Ok? So we will do some questions related to our HCF and LCM which come in our exams, that is, the questions which come in our exams are of this type only.

[00:00:28]So you just have to practice and concentrate and see how we will solve the questions. And I hope whatever practice you are doing, whatever preparation you are doing, it must be going well in all the subjects.

[00:00:40]If it is not working then improve it further because your exams are near so definitely practice. Work day and night to prepare for your exams. You should remain fully focused in preparing to crack your exam.

[00:00:52]Practice. You should do maths with discipline.

[00:00:56]Do it with consistency. So if we talk about question number one, now let us look at question number one. What do you have to tell us?

[00:01:02]We have to tell the greatest number by which we should divide the number? If we divide 135, 225 and 375 by that number, what will be our reminder? Five reminders came.

[00:01:14]Meaning how much will come in each case? Five came. Even if you do 135, you still get five. Even if you do 225, you still get five. And even if we do 375, our reminder will come to five. Ok? So how do you approach this type of question? You will do this type of questions. What will we do with the numbers given and the reminders asked for? Will give a minus. Like what has been given? 135 - 5 and 225 - 5 and what will happen to you? 375 - 5 okay? So this will be your 3130 this will become 220 and this will become your 370 now what will we do now what do we have to tell the greatest number we have to tell the greatest number which on dividing these numbers reminds that five will come out so what will we do is take their HCF HCF of 130 220 and 370 when you take its HCF it will come out to be 10 how will we find the HCF by prime factorization method now like we will do 130 2 * 6 = 12 2 * 5 = 10 ok then we will do 5 * 1 = 5 5 * 3 = 15 and now directly from which this will be our 13 will be correct now from which we will do 220 from two we will do 2 * 1 = 2 2 * 0 = 0 then from two we will do 2 * 5 = 10 and 2 * 5 = 10 after that from five we will do 5 * 1 = 5 * 1 = 5 and then we will do it from 11, so 11 * 1 = 11, after that we are talking about 370 70, if we talk about 370 then we will do it from two, so 2 * 1 = 2 2 * 8 = 16 and 2 * 5 = 10 ok 8 5 13 and if we plus one then we will get 14, so we will do it from five 5 * 3 = 15 and 5 * 7 = 35, after that one will come directly from 37.

[00:03:02]So if you look at it, what are the factors that came into play for 130? 2 5 And what about us? 13 If we talk about 220 then how much we have got is 2 * 2 * 5 * 11, on the other hand if we talk about 370 then we have got 2 * 5 * 37, so now we will see which of the three is common, which is our two, and what is common, our five is common, apart from that there is nothing common which is coming same in all the three, two is coming here, it is not coming only at the top and bottom, 13 is also coming only in one, it is not coming in both of these, similarly with 11 and 37, what happened to our HCF? It became 10. So how much HCF did we get? 10 came. So that is our greatest number.

[00:03:48]10 is our greatest number, if we divide it by this then how much reminder will we get? Five will come. So option number B will be our correct option for question number one.

[00:03:59]Ok? What were we asked? We have to tell the greatest number that if we divide the given numbers by that number, then how much reminder will come? Five will come. So what number is that? It is 10, when you divide 135 as 135 13 * 1 = 10 * 1 = 10, here it will come 3 5 10 * 3 = 30, so how much reminder will come, five, in the same way you will divide 225 by 10 and 375 by 10, then how much reminder will come, your five reminder will come, this is what we were asked. So option number B will be our correct option for question number one. Let us now move on to the next question. Question number here is its explanation.

[00:04:41]If we talk about question number two, what do we have to tell? Find the smallest number which when divided by 8, 12 and 15 leaves seven in each case. Now what do we have to tell that what is the smallest number when we divide it by? On 8th, 12th and 15th.

[00:04:59]So how many reminders did you get? Seven came in every case. Meaning, even if you start with 8, you will consume it with 12. And with whom will you do it?

[00:05:07]Even if we do it with 15, what will happen? The intake will come. So what will we do in such a case? We will take the LCM of 8, 12 and 15. So the LCM of this will be 120 for you. How much will you earn?

[00:05:22]Your LCM will be 120. How do you find the LCM? You can also find that out using the prime factorization method. 8 12 15 2 * 4 = 8, 2 * 6 = 12, 15 as it is. 2 * 2 = 4 2 * 3 = 6 15 as it is then we will do it by two 2 * 1 = 2 3 as it is 15 as it is we will do it by three 3 * 1 = 3 5 = 15 and now we will do it by five so you will do it 2 * 2 = 4 * 2 = 8 multiply 5 * 3 = 15 and 15 8 is what is yours? 120 So what is the LCM of 8 12 15? It is 120. Ok?

[00:06:00]So what will we do now? From 120 we will subtract one. Why? When we know that the reminder is our seven meanings, what is the meaning of seven reminder? Just one less than is the next multiple. What is? Just less than it is. Meaning from whom?

[00:06:20]From the next multiple. So 119 is our correct answer.

[00:06:25]So option number D will be our correct option for question number two. Ok?

[00:06:31]For question number two, our option number D will be correct. Let us now move on to the next question. Next, its explanation is given here. Third is Find the Greatest Number Which Divides 98 by 152 and 194 Leaving Same Reminder. Meaning we have to tell the greatest number. When we divide that number by what? If we divide 98, 152 and 194 by that number, we get the same reminder in every case.

[00:07:01]Now what do we have to remove to get the same reminder? The difference between these numbers will have to be calculated. So what will we do? 152 - 98 and 194 - 152 and 194 - how much will you get? 98. Ok? This will come to us. So how much will this cost us? 54 42 96 54 52 96 Okay 54 42 96 Now what will we find out, we will find its HCF, HCF of 54 42 and 96, the HCF that will come out is the same number that when you divide that number by this number, so what is your reminder, what will come out in every case, your sem will come out, so its HCF will come out to be six. How much will it cost? Six will come. You can also try to find it using the prime factorization method. Let's see.

[00:08:02]How much will it cost if you do 54? 2 * 2 = 4, 2 * 7 = 14, 3 * 9 = 27, 3 * 3 = 9 and 3 * 1 = 3 Now whose will we do? We'll do 42. 2 * 2 = 4, 2 * 1 = 2, 3 * 7 = 21 and 7 * 1 = 7 after that we will see 96. So 2 * 4 = 8, 2 * 8 = 16, 2 * 2 = 4, 2 * 4 = 8, 2 * 1 = 2, 2 * 2 = 4, 2 * 6 = 12, 2 * 3 = 6 and 3 * 1 = 3 Now look at the common ones. Too is here, too, and too. Now let's move ahead.

[00:08:30]Three is here also, it is here also. Come on, it is here too, it is here too and it is here too. Ok? So 2 * 3 we are talking about HCF here. 2 * 3 Now let's move ahead.

[00:08:41]Three is here but it is not here, it is not here. It is not here either. There is no consumption either. So how much did our HCF come? Six came. So how much did HCF come? It's six. It means when you divide this number by six, divide by 98, divide by 152, divide by 194, then the reminder that comes will be the same in every case.

[00:09:03]Ok? What will you do when you are given such a question? First of all we will find the difference between those numbers.

[00:09:06]Ok?

[00:09:10]What will we take after taking out the difference? We will take their HCF. Whatever HCF comes, that will be our greatest number. Where we talk about the greatest number, we find out the HCF.

[00:09:19]Wherever we talk about least number, we find out the LCM. The first question from this was our question number second, in that the least number was asked. So what did we find in the list? LCM was taken out. And in the first question, the greatest number was again discussed. So in the same manner, what was in the question was that reminder five should come. So we found the HCF by dividing by five minus one.

[00:09:41]What was there here, we were not given anything that we should get so many reminders. If you had asked that so many reminders should come, then we would have subtracted the reminders from those numbers. But what happens in this case is that we have been given numbers and we have been asked what will be the number if we divide these three numbers by that number so that our reminder comes out to be the same. Ok? So when will that be possible? Then first we will find out the difference between them.

[00:10:06]We will take the HCF of the difference which will be HCF. That's that number.

[00:10:11]Meaning six is ​​the number you get when you divide 98 by six.

[00:10:16]So the reminder that comes when we divide six by 152 or divide it by 194 will come when we divide 98 by six. So the same reminder will come in this condition. So this was your question number three. Now let's move forward to the next question. Talking about question number four, what do we have to find out? It is a straightforward question. We have to find out the LCM.

[00:10:42]Find out the least common multiple. Prime Factorization Method Is The Best Method To Find LCM Of Any Numbers. Ok? So this will be your 24 If we talk then whose do we want to take?

[00:10:55]24 of 36 and 48. Whose to take? 24 36 and 36 48 60. So let's do this for us 24 36 48 and 60. Ok? So we will do it with two. 2 * 1 = 2, 2 * 2 = 4, 2 * 1 = 2, 2 * 8 = 16, 2 * 2 = 4, 2 * 4 = 8, 2 * 3 = 6, 2 0 = 0 Then we proceed further. 2 * 6 = 12, 2 * 9 = 18, 2 * 1 = 2, 2 * 2 = 4 and 2 * 1 = 2, 5 = 10. Let's move ahead. It will be done again from two.

[00:11:23]2 * 3 = 6 will not be possible. So as it is.

[00:11:25]2 * 6 = 12 and 15 as it is. Because two will not make 15. Now what will happen with two? Three as it is. 9 As It Is.

[00:11:33]And 2 * 3 = 6 and 15 as it is. Who will do it now? From three. 3 * 1 = 3 3 * 3 = 9 3 * 1 = 3 and 3 * 5 = 15 Now what will it be? Then it will happen from three. So this has come and this has come 5 and this will come your 5 and this will come 1 1 so what is common in all of them? 1 has arrived.

[00:11:50]So now if we find its LCM then what will be the result? How much is 2 * 2 * 2 * 2? 1 2 3 4 1 2 3 4 * 3 * 3 * 5 We can also write it like this.

[00:12:05]2 to the power 4 * 3 to the power 2 * 5 We can also note it down this way.

[00:12:12]So when you multiply this, what will be your LCM? 720.

[00:12:17]How much did your LCM cost? 720. So option number D will be our correct option for question number four. Ok? This is our prime factorization method.

[00:12:30]Which method is this? Prime factorization is the easiest method to do what? To find out the LCM. Ok?

[00:12:38]Let us now move on to question number five. Let us talk about question number five here.

[00:12:43]So what do we have to tell? Find the largest number which divides 265 4 69 and 743 Leaving reminder how much should come?

[00:12:51]5 9 and 11 should come out to be 5 9 11. So how do we do it directly?

[00:13:00]What will you subtract from 265? Five will do. And what will you minus 4 from 69? Nine will do it.

[00:13:05]And what will we subtract from 743? 11 minus will do. Ok? So how much will come here? 260 will come here for us.

[00:13:16]This will be your 460 and how much will it cost you? This will come too. 2 This will come out to be three means 372 732 sorry I said it in reverse 732 now what will we do if we have to tell the largest number so what will we do find out the HCF of 260 460 and 732 so what will we do for this also we will use prime factorization method to find the HCF of all three so how much will this be 2 6 0 this will be 2 * 1 = 2 2 * 3 = 6 2 = 0 2 * 6 = 12 2 * 5 = 10 this will be our how much from 5 5 * 1 = 5 5 * 3 = 15 and this will be 13 * 1 = 13.

[00:13:53]Now whose do we do? Will do 46 0. This becomes 2 * 2 = 4 2 * 6 = 12 2 * 2 = 4 2 * 3 = 6 and 2 * 0 = 0 This becomes 2 * 1 = 2 * 1 = 2 * 5 = 10 Okay? 5 6 7 So who will have to do it? Will have to do it with five only. 5 * 2 = 10 and 5 * 3 = 15 If we do this with 23, we will get one.

[00:14:17]Who will we do it with after this? We will do it with 7 3 2.

[00:14:20]2 * 3 = 6 right? 2 * 3 = 6.

[00:14:24]2 * 6 = 12 2 * 6 = 12 then 2 * 1 = 2 2 * 8 = 16 and 2 * 3 = 6 8 4 12 will be done by three. 3 * 9 = 18 sorry 3 * 6 = 18 and 3 * 1 = 3 so it becomes 61. So, with whom will we do it directly? Let's do it from 61 only.

[00:14:46]So this came. So the meaning is too common here. It is here. It is here.

[00:14:50]So how much HCF did you get? Four came.

[00:14:52]How much HCF came? Four came. So four is the number when we divide by what?

[00:14:57]We will divide this number 265 by four.

[00:15:00]So how often will the reminder come? Five. And if we divide 469 by four, what will be the reminder? Nine. And if we divide 743 by four, what will our reminder be? 11. So this was asked in this question.

[00:15:13]Ok? Ok? I hope now you must be understanding how we will solve the question. How to find out HCF LCM. How do we tell the largest number, the greatest number, the least number or the smallest number. Okay, this was question number five. Now let's move ahead to the next question. Three numbers are in the ratio. Three numbers are given in the ratio.

[00:15:32]That is 3 4:5 okay? What is their LCM? Their LCM is 420. So we have to tell those numbers. Meaning, do we know what we take in LCM? 3x 4x 5x So if we see how much is our 3x, let us see how much is 4x and then we see how much is 5x, then what will be the LCM, our 3 * 4 * 5 * x will be equal to 420, okay, so what will we do now, 4 * 1 = 4 4 * 1 = 4 and 4 * 0 and 4 * 5 = 20 4 * 5 = 20, after this we will do, then 5 * 2 = 10 and 5 * 1 = 5 and this will become 3 * 7 = 21.

[00:16:14]So what is the value of x? Seven has come.

[00:16:16]So what will be our number? 3 * 7 4 * 7 and 5 * 7 it means 21 28 and 35 21 28 35 it means option number C will be correct for our question number six.

[00:16:33]Now let's move ahead to the next question. That is question number seven. If we talk about question number seven, what is given in question number seven?

[00:16:41]We have to tell the smallest number divisible by 12 18 24 and 30 leaving a reminder that how much should our six come, that is, a reminder how much should your six come, so what will we do in this, we will take the LCM, okay, we will take the LCM, whose LCM will we take the LCM of 12 18 24 and 30, so what will be the LCM, its prime factorization of 12 18 24 30 2 * 6 = 12 2 * 9 = 18 2 * 1 = 2 2 * 2 = 4 5 = 10 then to 2 * 3 = 6 ok 2 * 3 = 6 9 as it is 2 * 6 = 12 and 15 as it is then to 2. This will be three. This will happen, right? This will be three.

[00:17:30]This will be 15. After that we will do it with three, 1 3 1 and 3 5, now we will do it with three.

[00:17:36]This will become a forest. This will become a forest. This will be five. Then we will do it from five. So how much will 1 1 cost? 1 1 will come. What is the power of It Means To? It is three. What is the power of three? There is two. And there's five. What is?

[00:17:50]This will be multiplied among themselves. Let's see once again.

[00:17:51]2 * 6 = 12 2 * 9 = 18, 2 * 1 = 2, 2 * 2 = 4, 2 * 1 = 2 * 5 = 10, 2 * 3 = 6, 9, 2 * 6 = 12 and 15 will then do 9 as it is.

[00:18:00]From 2 * 3 = 6, 15, 36. Ok? So when you multiply 2 to the power 3, the LCM you get will be 360.

[00:18:08]How much will your LCM be? 360.

[00:18:12]What will be your LCM? 360 will come. So what do we have now? 360 is that number which when we divide it completely by 12, it will be completely divisible. If you divide 360 ​​by 18, it will be completely divided. If you divide 360 ​​by 24, it will be completely divided. And even if we divide it by 30, it will still be completely divisible. But what do we need? Reminder six is ​​needed in every single case. So what do we have to do?

[00:18:37]If I add six to 360. It means 366 will be the number when I divide it by what? Even if I divide by 12, the reminder will be six. Even if I divide by 18, the reminder will be six. Even if I divide by 24 or 30, the reminder will be six. It means option number B will be our correct answer for question number seven.

[00:18:56]Ok? When asked how much the reminder is and the smallest number. Smallest number means what will we find? Least number that is LCM. LCM will find out.

[00:19:05]So we found out the LCM which came out to be 360 ​​but what is LCM? LCM is the common number which when divided by 12 18 24 30 will be completely divisible.

[00:19:16]But we need reminder six. So what did we do? Added six to it.

[00:19:20]So it is obvious that when we added six to it, it became 366. So when we divide that by 12 18, it will give us the reminder six.

[00:19:28]Ok? So our option number seven is completed. Its complete explanation is also available here. Now let's move ahead.

[00:19:34]Next is find the greatest number that divides this much by that much and leaving the same reminder same what will we do first we will find the difference how much will it come 180 - 144 we will do 216 - 180 and what will we do by subtracting 216 we will do 144 so the number that comes when we subtract that is 3672 and 72 that is 36 72 and this is also 72 so what will we find out its greatest number means it will be about HCF. So whose HCF will come? 36 72 and 72, what will be your HCF? Only 36 will come. So 36 will be that number.

[00:20:15]Ok? 36 will be the number which will divide these and the same reminder will come. So option number A will be our correct answer for question number eight. Now let's move forward to the next question. That is question number nine. Two numbers are in the ratio. There HCF is six. Find the numbers. What are given? Two numbers are given.

[00:20:36]What do we have to tell them? HCF.

[00:20:38]What is the given HCF? It's six.

[00:20:43]How much is HCF? It's six. So what will those numbers be for us?

[00:20:49]How much? What is that given? 5:7 it means 5 * 7. And what will be the second number? 7 * 7 it means 35 and 49 are our numbers.

[00:21:00]It means 35 and 49 7 * 5 = 35 and 7 * 7 = 49 this is what it will be sorry it is six, not our five it is six 5 * 6 = 30 and 7 * 6 = 42 so option number C will be correct for question number nine when this kind of question comes what to do you have been given HCF okay numbers have been given you two numbers are in ratio okay so this is what HCF means what will HCF mean? Now look, you will take their HCF of 30 and 42. Ok? If you find out its HCF then it will be 2 * 1 = 2 * 5 = 10 This will become 3 * 5 = 15 and 5 * 1 = 5 Then we will do 2 * 2 = 4 2 * 1 = 3 * 7 = 21 and 7 * 1 = 7 So if you find out the HCF of these numbers then what will be the result? Only six will come. It means six is ​​the common number for both.

[00:21:51]What about both of them? That is a common number. So if we multiply that common number by them, what will we get? The numbers will come brother, how many are there? 30 and 42 If you calculate the ratio of 30 and 42, what will it be? Only 5 and 7 will come. It means only 5 7 will come. So what are our numbers? 30 and 42. So option number nine and option number C of question number nine will be our correct answer.

[00:22:13]Now let's move forward to the next question. This is our next question. Find the least number. We have to tell the least number.

[00:22:20]Which man divided by 16, 20 and 24 leaves reminder four. What we need to tell is that that reminder four should come. So what will we do? Whose LCM will you take? 16, 20 and 24. Ok? What will come to us? Of 16, 20 and 24. 2 * 8 = 16, 2 * 1 = 2, 2 * 1 = 2, this becomes 2 * 4 = 8, 2 * 5 = 10, 2 * 6 = 12, this becomes 2 * 2 = 4, this becomes 2 * 3 = 6, this becomes 2 * 1 = 2, 5 and this becomes three as it is. This will become 3 * 1 This will become 5 and 5 here ok so 2 to the power 4 * 3 * 5 it means 2 * 2 = 4 * 2 = 8 * 2 = 16 2 * 2 = 4 2 * 2 = 2 * 2 * 2 * 2 = 4 * 2 = 8 2 = 16 16 * 3 * 5 = 15 so how much will you have?

[00:23:15]16 * 15 means 240, so what will be your LCM? 240 will come.

[00:23:21]How much do we need reminders? I need four. Because this is the number which when divided by less will be completely divisible. So what will we do? 240 + 4 will do. It means 244 is that number. What will be the reminder when we divide that number by 16 20 24?

[00:23:37]Four will come. So this was our question number 10th today. And our last question is about power punch. You should practice like this.

[00:23:47]Practice a lot. Practice a lot so that you know which approach you will use as soon as you see the question.

[00:23:52]You have to find the LCM, find the HCF.

[00:23:54]You should understand that question completely in every way.

[00:23:56]Meaning you have to feed your things like this. Ok? So, now we will meet in the next video with a new topic. Till then you should do your practice. Ok? Work hard. And you should put your heart and soul into every subject in every way so that later you do not feel that if you had practiced a little more or worked a little harder then it would have been done, but it will be done because you are associated with GDC. You have to work hard, just keep practicing and stay connected with us and take care of yourself.

[00:24:23]Take care. See you in the next video. Thank you.