The lunar cycle is closer to 29.53 days. A lot of moon phase clocks have gears with 59 teeth (as did the Antikythera mechanism) that closely approximate two lunations. The Gregorian calendar has a sidekick lunar calendar good to about one day in 8,000 years on average, which is even better than the Gregorian calendar’s approximation of the solar year (365 + 1/4 -1/100 + 1/400 = 365.2425), which is only good to about one day in 3000 years. The lunar calendar is used with the Gregorian Calendar to calculate the date of Easter.
The synodic month (which is the familiar one) is 29.53, the sidereal month is 27.something. :^)