When solving a Rubik's Cube, a common algorithm in speedcubing is the "sexy move," in which the solver performs the moveset $R$ $U$ $R'$ $U',$ meaning, "rotate the rightmost face $90^{\circ}$ clockwise, then the uppermost face $90^{\circ}$ clockwise, then the rightmost face $90^{\circ}$ counterclockwise, then the uppermost face $90^{\circ}$ counterclockwise."

How many times will a solver have to perform the "sexy move," starting in a solved state, before he returns to the solved state again?

Learn more about Rubik's move notation here.