2013 AMC 10B Problems/Problem 9

Problem

Three positive integers are each greater than , have a product of , and are pairwise relatively prime. What is their sum?

$\textbf{(A)}\ 100\qquad\textbf{(B)}\ 137\qquad\textbf{(C)}\ 156\qquad\textbf{(D)}}\ 160\qquad\textbf{(E)}\ 165$ (Error compiling LaTeX. Unknown error_msg)

Solution

The prime factorization of is . These three factors are pairwise relatively prime, so the sum is