Question

The least common multiple of two numbers is 60 and one of the numbers is 7 less than the other. What are the numbers?

Answer 1

The two numbers are `5` and `12`.

Explanation:

As the least common multiple of two numbers is `60`, the two numbers are factors of `60`.

Factors of `60` are `{1,2,3,4,5,6,10,12,15,20,30,60}`

As one of the numbers is `7` less than the other, the difference of two numbers is `7`

Among `{1,2,3,4,5,6,10,12,15,20,30,60}`, `3` & `10` and `5` & `12` are the only two pair of numbers whose difference is `7`. But Least common multiple of `3` and `10` is `30`.

Hence, the two numbers are `5` and `12`.