Question

How do you find the smallest positive integer k such that 1350k is a perfect cube?

Answer 1

A cube is x*x*x
prime factor 1350
1350*k
5*270*k
5*3*90*k
5*3*3*30*k
5*3*3*3*10*k
5*3*3*3*2*5*k
what value does k have to be to have three of each prime factor?
k = 5*2*2 = 20

Then 1350*20 = 27,000 = (5*3*2)^3