1986 AIME Problem 14

The shortest distances between an interior diagonal of a rectangular parallelepiped, P, and the edges it does not meet are 2\sqrt{5}, \frac{30}{\sqrt{13}}, and \frac{15}{\sqrt{10}}. Determine the volume of P.

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.