jmc

Question

The least common multiple of two numbers is 3780, and the greatest common divisor is 18. Given that one of the numbers is 180, what is the other number?

Accepted Answer

We use the identity (a,b) lcm[a,b] = ab for all positive integers a and b. We are told that (a,b) = 18, and lcm[a,b] = 3780, so ab = 18 3780. If one number is 180, then the other number is 18 3780/180 = 378.