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?
I know that the least common multiple (LCM) of two numbers is the smallest positive integer that is a multiple of both numbers, and the greatest common divisor (GCD) is the largest positive integer that is a divisor of both numbers. I also know that there is a formula that relates the LCM, GCD, and the two numbers: LCM(a,b) = (a*b) / GCD(a,b), where a and b are the two numbers. So, if I plug in the given values, I get: 3780 = (180*b) / 18. Simplifying, I get: 3780 = 10*b, or b = 378. Therefore, the other number is 378. 