Q) Find the greatest 3-digit number which is divisible by 18, 24 and 36.

Ans:

Here, this question is slightly tricky one. We need to first find lowest number and then find its largest multiple with 3 digits.

Hence, we need to find LCM, not HCF.

Let’s start with LCM of 18, 24, 36.

By prime factorisation method, we get LCM as 72.

Now since we need to find largest 3 digit number, we will divide smallest 4 digit number (1000) by 72 and subtract the remainder from 1000 to get the answer.

Hence,

Hence the required number is 1000 – 64 = 936

Therefore, the greatest 3 digit number divisible by 18, 24 and 36 is 936.