A rectangular box has faces with areas of 12,15, and 20 square units. What is the volume of the box?

First find the side lengths of the box by factoring each area:

12: 1, 2, 3, 4, 6, 12

15: 1, 3, 5, 15

20: 1, 2, 4, 5, 10, 20

Find 3 numbers that both have 2 sides have in common and can multiply to make the areas of the faces:

12: 3 * 4

15: 3 * 5

20: 4 * 5

Sides: 3, 4, and 5

Then multiply to get the volume:

3 * 4 * 5 = 60 units^2