>A lunar cycle is 27 days plus a little less than 8 hours.

That is the lunar orbital period, but from earth it appears as though it takes ~29.5 days for the moon to cycle through its phases(this longer period is termed the 'lunation'). The difference is due to the earth-moon system orbiting around the sun, so by the time the moon has completed it's orbital period around the earth, the earth-moon system has rotated around the sun ~1/13 of its period, changing the angle at which the moon is illuminated, which is what determines the apparent phase of the moon as observed from earth. So the moon has to travel a bit further than its full orbit to appear as though its completed a cycle as viewed from earth.

The lunar cycle is 29.5 days, https://en.wikipedia.org/wiki/Lunar_phase