Now here we are looking for a Set S of numbers n such that \(n^2\) is multiple of 24 and 108.

Lets take one such case Least Common Multiple of 108 and 24 is 216.

\(n^2\) = 216
n = 6\(\sqrt{6}\).

This is not an integer however if we multiply 216 by any number it is still divisible by 24 and 108. So we multiply by 6 and repat the above steps to find n. So n =36.

Now n= 36 is one of the number in set S.

Hence all the options that divide n =36 are correct. Hence option A and C.
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Sandy
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LCM of 108 and 24 is 216 = 2^3*3^3. As n^2 is a square, the least value n^2 can take is 2^4*3^4 = 6*216 = 36 * 36, so n should be at least 36 or multiples of 36. So any factor of 36 should always divide n. Hence A and C are correct.