2021 AMC 12B Problem 14

Let ABCD be a rectangle and let \overline{DM} be a segment perpendicular to the plane of ABCD. Suppose that \overline{DM} has integer length, and the lengths of \overline{MA},\overline{MC}, and \overline{MB} are consecutive odd positive integers (in this order). What is the volume of pyramid MABCD?

\textbf{(A) }24\sqrt5 \qquad \textbf{(B) }60 \qquad \textbf{(C) }28\sqrt5\qquad \textbf{(D) }66 \qquad \textbf{(E) }8\sqrt{70}

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