Question

find the smallest number of 12 must be multiplied to obtain a perfect cube.

Answer 1

Your question might be, " find the smallest number with which 12 must be multiplied to obtain a perfect cube"

If this is your question then answer is:

18

If you will factorize, 12,i.e., do prime factorization of 12; then you will get:

12 = 2x2x3

since a number is perfect cube, when it can be expressed as the product of triplets of equal factors, we need to make triplets of 2 and 3 because 2 and 3 are the numbers you get after factorization. Here one 2 and two 3 are needed to make triplets of 2 and 3. Therefore the number is 2x3x3 which is 18.

After multiplying 12 with 18 we get:

216; which is the perfect cube of 6.

Hope it helps!