I need help on this question. What is the smallest positive integer n such that 2n is a perfect square and 3n is a perfect cube?

Question

I THINK THE ANSWER IS 1, IS THIS CORRECT?

Answer 1

Consider the prime factorization of n. How many factors of 2 does this need to contain and how many factors of 3?

Answer 2

prime factorization for 36

Answer 3

prime factorization for 180