Correct approach: The gear with 48 rotations/min makes a rotation every $ \frac148 $ minutes. The other every $ \frac172 $ minutes. They align when both complete integer numbers of rotations and the total time is the same. So $ t $ must satisfy $ t = 48 a = 72 b $ for integers $ a, b $. So $ t = \mathrmLCM(48, 72) $. - Veritas Home Health