1990 AIME Problem 5

Let n^{}_{} be the smallest positive integer that is a multiple of 75_{}^{} and has exactly 75_{}^{} positive integral divisors, including 1_{}^{} and itself. Find n/75^{}_{}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.