Hi Melguy,
This is a good example for prime factorization question type in GMAT.
Here first we need to do is prime factorize 240.
240 = 2^4 * 3 * 5
Given k^3 is divisible by 240, so it has to be perfect cube.
To be a perfect cube, after prime factorizing a number the power of the primes should be divisible by 3,
So we have to multiply minimum 2^2 * 3^2 * 5^2 with 240, so that we get the power of primes divisible by 3.
So k^ 3 = 2^6 * 3^3 * 5^3 ,
So k = 2^2 * 3 * 5
K = 60.
We can multiply any multiples of 2, 3 and 5 where the power is divisible by three. But since question is asking least possible value of k, we should have multiply to 240 minimum 2 two's , 2 three's and 2 five's.
Another way of solving this question, use the answer choices.
Since question asks about least possible value of k, start with least in the answer choices.
A.K = 12. Here 12 ^ 3 is certainly not divisible by 240. Since it has no zero.
B.K = 15. Here 15 ^ 3 is certainly not divisible by 240. Again its not have a zero.
C.K = 60. Here 60 ^ 3 will divisible by 240. We can quickly prime factorize and check this. So the
answer is C.
Hope it is clear
