How often to the hands of a clock line up?

How often to the hands of a clock line up?

How often do the hour and and minute hand of an analog clock point in the same direction? The hands start pointing the same direction at midnight, then the hour hand moves clockwise (!) by 360° in 12 hours. The minute hand moves clockwise at the rate of 360° in one hour. So when does the minute hand, moving at 360°/ hour lap the hour hand moving at 30° per hour? When 360t = 30t mod 360 or equivalently 12t = t mod 12 which means t is a multiple o…