MathDB

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.

4