Question

A number $x$ is equal to $7\cdot24\cdot48$. What is the smallest positive integer $y$ such that the product $xy$ is a perfect cube?

Answer 1

Answer: 588

Explanation:

Answer 2

Take the prime factorization of
`x`.

`x = 7*24*48 = 7*(2^3*3)*(3*2^4) = 2^7*3^2*7`

If
`xy` is a perfect cube, then the smallest
`y` that makes this happen is
`y=2^2*3*7^2 = \boxed{588}`. We "complete" the cube by introducing just enough factors to get each prime power to be a multiple of 3.