[RESOLVED] Perfect cube???

[Yunie]

Expressed as the product of prime factors


540 = 2^2 x 3^2 x 5 and 72 = 2^3 x 3^2


Use these results to find

the smallest integer, t, such that 540t is a perfect cube.


I have looked through the working solutions but I don't understand the steps on why it is been done in that way. Can anyone explain it to me or maybe you could do it in another way so that I can understand it better? Thanks a lot.


Working solutions:

540t = 2^2 x 3^2 x 5 x (2x5^2)
=> t = 2 x 5^2
t = 50


Please answer this thread asap. Thanks a lot.