2022 AMC 12A Problem 18

Let T_k be the transformation of the coordinate plane that first rotates the plane k degrees counterclockwise around the origin and then reflects the plane across the y-axis. What is the least positive integer n such that performing the sequence of transformations T_1, T_2, T_3, \ldots, T_n returns the point (1,0) back to itself?

\textbf{(A) } 359 \qquad \textbf{(B) } 360\qquad \textbf{(C) } 719 \qquad \textbf{(D) } 720 \qquad \textbf{(E) } 721

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