2016 AIME II Problem 4

An a \times b \times c rectangular box is built from a \cdot b \cdot c unit cubes. Each unit cube is colored red, green, or yellow. Each of the a layers of size 1 \times b \times c parallel to the (b \times c) faces of the box contains exactly 9 red cubes, exactly 12 green cubes, and some yellow cubes. Each of the b layers of size a \times 1 \times c parallel to the (a \times c) faces of the box contains exactly 20 green cubes, exactly 25 yellow cubes, and some red cubes. Find the smallest possible volume of the box.

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.