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Divisors

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Divisors

by MBA.Aspirant » Sun Jun 26, 2011 11:30 pm
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?

Check all that apply

A) 12
B) 24
C) 36
D) 72
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by Frankenstein » Mon Jun 27, 2011 12:35 am
Hi,
n^2 is multiple of 24 and 108
24 - 12*2
108 - 12*9
So, LCM of 24 and 108 is 12*2*9 = 2^3*3^3
n^2 is a multiple of 2^3*3^3. So, n2 should be of the form 2^4*3^4*p^2 where p is any positive integer.
So, n is of the form 2^2*3^2*p = 36p
Only, 12 and 36 satisfy for all values of n
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