2011 AMC 12B Problems/Problem 5
Problem
Let be the second smallest positive integer that is divisible by every positive integer less than . What is the sum of the digits of ?
Solution
must be divisible by every positive integer less than , or and . Each number that is divisible by each of these is is a multiple of their least common multiple. , so each number divisible by these is a multiple of . The smallest multiple of is clearly , so the second smallest multiple of is . Therefore, the sum of the digits of is