Question

What is the smallest positive integer $n$ such that $3n$ is a perfect square and $2n$ is a perfect cube?

Answer 1

108

Explanation:

Since 3n is a perfect square, that means that n has to be a multiple of 3. Since 2n is a perfect cube, then n has to be divisible by 2^2=4. Since n is a multiple of 3, then n also has to be divisible by 3^3=27. Therefore, the smallest value for n is 4*27=108.