Question 391576
{{{180 = 2^2*3^2*5}}}.  Hence for the smallest positive value of X that will make 180X a perfect cube is {{{2*3*5^2 = 150}}}.  As a check, {{{180X = (2^2*3^2*5)*(2*3*5^2) = 2^3*3^3*5^3 = (2*3*5)^3 = 27000}}}