2024 AMC 12A Problem 12

The first three terms of a geometric sequence are the integers a,\,720, and b, where a<720<b. What is the sum of the digits of the least possible value of b?

\textbf{(A) } 9 \qquad \textbf{(B) } 12 \qquad \textbf{(C) } 16 \qquad \textbf{(D) } 18 \qquad \textbf{(E) } 21

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