2021 Fall AMC 12A Problems/Problem 8
Problem
Let be the least common multiple of all the integers through inclusive. Let be the least common multiple of and What is the value of
Solution
By the definition of least common mutiple, we take the greatest powers of the prime numbers of the prime factorization of all the numbers, that we are taking the of . In this case, Now, with the same logic, we find that because we have an extra power of and an extra power of Thus, . Thus, our answer is
~NH14