AMCAMC 12number theoryleast common multiplegreatest common divisor2020 AMC 12A2020 AMC
Problem Statement
How many positive integers n are there such that n is a multiple of 5, and the least common multiple of 5! and n equals 5 times the greatest common divisor of 10! and n?<spanclass=′latex−bold′>(A)</span>12<spanclass=′latex−bold′>(B)</span>24<spanclass=′latex−bold′>(C)</span>36<spanclass=′latex−bold′>(D)</span>48<spanclass=′latex−bold′>(E)</span>72