2018 AMC 10A Problem 22

Let a, b, c, and d be positive integers such that \gcd(a, b)=24, \gcd(b, c)=36, \gcd(c, d)=54, and 70<\gcd(d, a)<100. Which of the following must be a divisor of a?

\textbf{(A)} \text{ 5} \qquad \textbf{(B)} \text{ 7} \qquad \textbf{(C)} \text{ 11} \qquad \textbf{(D)} \text{ 13} \qquad \textbf{(E)} \text{ 17}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.