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

Thank you @Veeresh.

Add 3,13,23,33 to 2497 separately.

2494 + 3 = 2500 likewise then these factors 5, 6, 4, 3 divided to the result it must be 0 i.e. 2497 + 23 = 2520 it is divided by 5, 6, 4, 3.

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).

After LCM is 60.

Now we want to know which number is added to make divided 2497 with 60.

2497/60 = 41 but there is remeder is 37 and we want to fully divided so add 23 from the option.

Best of luck.

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.

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.

How to find lcm? How it comes 60? Please help.

How to divide it without Remainder?

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.

Please divide 2497 by 60 and the remainder is 41.6166666 not 37.

So 23 is not correct answer.