Let S be the set of all positive integers n such that n^2 is a multiple of both 24 and 108. Which of the following integers are divisors of every integer n in S ?
Pick:
A) 12 B) 24 C) 120 D) 72 E) 182
4 = 2^3*3;   108 = 2^2*3^3.   The smallest perfect square (n^2) which is a multiple of both 24 = 2^3*3 and 108 = 2^2*3^3 is 2^4*3^4, thus the smallest n is 2^2*3^2 = 36. So, only 12 is a divisor of all integers in S.   12nswer: 12.
<result>A</result>
Let S be the set of all positive integers n such that n^2 is a multiple of both 24 and 108. Which of the following integers are divisors of every integer n in S ?