AMC 10A 2026 (Problem 11)
Gary writes down six distinct positive integers: , and a three-digit number . One of those six numbers is the least common multiple of all six of them. What is the sum of all possible values of ?
Case 1: is the LCM.
So is a multiple of . Since is a three-digit number and all six numbers are distinct,
Case 2: One of is the LCM of all six numbers.Since the LCM must be a multiple of , the only possibility is . Therefore,
So is a multiple of . Since is a three-digit number and all six numbers are distinct,
By Hints 2 and 3,
(D) 2280