Question

Laura must choose a number between 67 and 113 that is a multiple of 5, 8, and 10. Write all the numbers that she could choose. If there is more than one number, separate them with commas.

Answer 1

80 is the only one that I find.

Answer 2

First, note that every multiple of 10 is a multiple of 5, so we can throw out 5. Thus, we're looking for multiple of 8 and 10. Since their least common multiple is 40, we're looking for multiple of 40 between 67 and 113.

If we list the multiples of 40, we get 40, 80, 120, ... Note that 80 is the only number in that list between 67 and 113. Thus, 80 is the only possibility.