1996 AIME Problem 14

A 150\times 324\times 375 rectangular solid is made by gluing together 1\times 1\times 1 cubes. An internal diagonal of this solid passes through the interiors of how many of the 1\times 1\times 1 cubes?

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.