When divided by 2 we get perfect square
(2^n * 3^m) / 2 = 2^(n-1) * 3^m is a perfect square
(n-1) and m are divisible by 2
When divided by 3 we get perfect cube
(2^n * 3^m) / 3 = 2^n * 3^(m-1) is a perfect cube
n and (m-1) are divisible by 3
(n-1) divisible by 2 & n divisible by 3 → n = 3
m divisible by 2 & (m-1) divisible by 3 → m = 4
Number = 2³ * 3⁴ = 648
648/2 = 324 = 18²
648/3 = 216 = 6³
ANSWER: 648