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2016 AMC 12B Problems/Problem 24

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Problem

There are exactly $77,000$ ordered quadruplets $(a, b, c, d)$ such that $GCD(a, b, c, d) = 77$ and $LMC(a, b, c, d) = n$ . What is the smallest possible value for $n$ ?

$\textbf{(A)}\ 13,860\qquad\textbf{(B)}\ 20,790\qquad\textbf{(C)}\ 21,560\qquad\textbf{(D)}\ 27,720qquad\textbf{(E)}\ 41,580$

Solution

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