MathDB
GCD & LCM Problem

Source: 2022 AMC 10A #7 / 2022 AMC 12A #4

November 11, 2022
number theory2022 AMC2022 AMC 10a2022 AMC 12AAMC 10AMC 12AMC

Problem Statement

The least common multiple of a positive integer nn and 18 is 180, and the greatest common divisor of nn and 45 is 15. What is the sum of the digits of nn?
<spanclass=latexbold>(A)</span>3<spanclass=latexbold>(B)</span>6<spanclass=latexbold>(C)</span>8<spanclass=latexbold>(D)</span>9<spanclass=latexbold>(E)</span>12<span class='latex-bold'>(A) </span>3\qquad<span class='latex-bold'>(B) </span>6\qquad<span class='latex-bold'>(C) </span>8\qquad<span class='latex-bold'>(D) </span>9\qquad<span class='latex-bold'>(E) </span>12