Hi Pretz,
In the original question, we're essentially looking for the smallest multiple of 32 that is a perfect square....
32(2) = 64......which is 8^2.
Using prime factorization, we know that 32K = (2^5)K
By making K = 2, we have (2^5)(2) = 2^6
We can then break 2^6 into 2 equal "pieces": (2^3)(2^3) which equals (8)(8)
To answer your question, we're going to use a similar approach:
We're looking for the smallest multiple of 144 that is a perfect cube....
144K = (2^4)(3^2)K
By making K = 12, we have (2^4)(3^2)(2^2)(3) = (2^6)(3^3)
We can break this down into 3 equal "pieces": [(2^2)(3)][(2^2)(3)][(2^2)(3)] = (12)(12)(12)
GMAT assassins aren't born, they're made,
Rich
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