Aptitude - Problems on H.C.F and L.C.M - Discussion

1. When 2497 must be added by some number say n.

2. Since it must be divisible by 3, 4, 5 and 6 we know that LCM is the multiple of all these so we take LCM which is 60.

3. Now we divide 2497 by 60 we get remainder as 37.

4. Which we know that if we subtract => 2497 - 37 = 2460 which is perfectly divisible by 60 (Hence divisible by 3, 4, 5 and 6).

5. But the question is as what is to be added so when, we even know that the next number divisible by 60 after 2460 is 2520 (which is 2460 + 60) we already have 2497 + n = 2520 where n = 60 - 37 => 23 so 2497 + 23 = 2520 which is perfectly divisible by 60 (which means that divisible by 3, 4, 5and 6).

Now accordingly we get lcm of 5,4,6 and 3 as 20. Now as it says that when wats the least number to be added with 2497 so that it get divided by 60 completely.

Now when we divide 2497 by 60 we get remainder as 37(left over). Now 37 would not be the remainder or left over and be divided by 60 completely if 33 more was there 23 more was there with 37(23+37=60).

So we got 23 by equation calculating 60-37 as that is the only amount needed to add with 37 so that its divisible by 60.

So in other words 23 is the only amount to be added to 2497 to get it fully divided by 60(2497+23).

Guys whoever did not understand this, refer this;.

Any such problem comes, the first step is to find the lcm of the factors given.

Next step is to divide this LCM obtained by the dividend given in the question.

Now whatever remainder you obtain, subtract it from the dividend. The resulting number will be exactly divisible by the LCM.

Since they have asked the question what must be subtracted, hence the required answer will be the difference between your LCM and the remainder. In this case, 60 - 37 = 23.

I hope you understand reading this reply.

LCM is 60.
The sum is of the form 60k.
i.e. 2497 + n = 60k

Try through the options:
A]3
2497+3= 2500. It is not divisible by 60.
B]13
2497+13= 2510. It is not divisible by 60.
C]23
2497+23= 2520. It is divisible by 60.

The least no is asked so no need 2 try the D option.

Now this sum of 2520 is divisible by 60. So we added 23 to the given no 2497 so that the sum is divisible by all the nos 5,6,4 & 3.

Dividing 2497 by the lcm of 5, 6, 4, 3 (which is 60, btw) gives 37 as remainder. (41 is the quotient)

Subtracting 37 from 2497 we get 2460 which is the nearest number divisible by 60.(2520 is the next number)
2460+60=2520.

Break the equation (2460+37)+23=2520
2497 + 23= 2520.

23 is the least number that should be added to 2497 so that the sum is divisible by 60!.

very simple

Look 60 is the common number divisible by 5,6,4& 3
ie LCM of 5,6,4,3

now when we divide 2497/60, we get 37
That means 2497 has got 37 number of 60's.

and to make it perfectly divisible by 60, we have to
add (60-37=23) more to 2497

by which the number becomes 2497+23=2520

and 2520 is divisible by 60, then it is defiantly divisible by 5,6,4,3.

i hope now its easy to understand.

Simple, if a number is divisible by 4 numbers, then the number will also divisible by their least common multiple. say, 50 is divided by 2,5,10,25.

Then lcm of (2, 5,10,25) is 50. So, 50 is divisible by 50.

So in the question, the number will divisible by lcm of the numbers, 60.
60k= 2497 + n.

We have to add a number for 60 to completely divide 2497.
Check options its 23.

2497 + 23 = 2520/60.

An easy method to find the lcm:

Suppose the numbers are 12, 24, 36.

Just consider the greatest number of these three and check whether the other two numbers are divisible by it.

Here 12 and 24 are not divisible by 36. Now take the 2nd multiple of 36 i.e. 72 and see if 72 divides 12 and 24. Here it does divide. Hence that is the lcm.

Try for other numbers and see the result.

@Tanya.

60 is the LCM of 5,6,4,3.

The keyword being Least in LCM. So any multiples of 60 should also be a multiple of 5,6,4,3.
So we divide 2497 by 60. Now we get 37 as remainder and quotient as 41. The question is how much should we ADD, so we find the next product which is 42.

Hence, (60*42) - 2497=23. This is the answer.

Hope you understood!

41.6166666 is not the remainder, it is the quotient. Divide it without using calculator by simple division method.

60)2497(41
    240
    ----
    97
    60
    ----
    37 is the remainder.