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Shortcut:

It's rather long to try and find a multiple of 24 for which it will be equal to 6^3 = 216

I find it much easier to reason like so:

1) Prime factorize 24: 2^3 x 3
2) 6 is 2 x 3
3) We can see the power we need right away - 3 - we can answer directly -> answer (C)

In order to be able to divide 6 by 2^3 x 3 we need its powers of its primes to be greather that or equal to 3, i.e. n ≥ 3
But since the stem asks us for the smallest value of n, the answer is 3.

When we divide 2^3 x 3^3 (6^3) by 2^3 x 3 (24) we are left with 3^2 (9) which is equal to the number you would have to find if you were to multiply 24 by hand.
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