Question

What should be divided by 240 to make it a perfect cube?​

Answer 1

So let's break down 240 into primes to help determine what extra prime factors we need to make 240n a perfect cube. In order to make 240n a perfect cube, we need two more 2s, two more 3s and two more 5s. Thus, the perfect cube that is a multiple of 240 is 2^6 x 3^3 x 5^3. Thus, the minimum value of k is 60.