A worker is stacking boxes. One stack has boxes that are 2 inches high. The other stack has boxes that are 5 inches high. At what height will the two stacks of boxes be equal in height?

10 inches.

Step-by-step explanation:

One stack has boxes that are 2 inches high, then the height of this stack can be only multiples of 2 inches.

The other stack has boxes that are 5 inches high, then the height of this stack can be only multiples of 5 inches.

The height of both stacks will be the same for all the common multiples of 2 and 5.

Because 2 and 5 are prime numbers, all the common multiples between 2 and 5 will be direct products of these two numbers.

Like 2*5 = 10

is both a multiple of 2 and 5 (is the first common multiple)

Then we can use stacks of 10 inches.

Such that, for the stack where each box is 2 inches high, we need:

10in/2in = 5

5 boxes.

And for the stack where each box is 5 inches high, we will need:

10in/5in = 2

2 boxes.