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.