how long does it take the moon to cycle through all of its phases

The Moon takes about 29.5 days to cycle through all of its phases, which is called a lunar month or synodic month. This period includes the progression through the eight phases: new moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, third quarter, and waning crescent. The lunar cycle is longer than the Moon's orbital period around Earth (27 days) because Earth is also orbiting the Sun, so the Moon has to travel a bit further to complete a full phase cycle.