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


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, \frac{1000}{72} = 13 \frac{64}{72}

Hence the required number is 1000 – 64 = 936

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

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