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

@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!

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.

Why 60-37? Explain.

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!.

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).

On dividing 2497 by 60 so the remainder will not become 37. The right remainder will become 41.61.

So why it is 37 here, could you please explain?

The remainder becomes 37.

60*41=2460+60=2520-2497 = 23.

Great answer, Thanks @Anita.

Why we divide 2497 by 60? Please explain.