Average moon cycle is about 29.5 days.
The average menstrual cycle is 28 days, so yes, some women will sync their cycles with the moon, most most cycles will not synchronize with the moon!
No correlation between lunar and menstrual cycle – an early report by the french physician J. A. Murat in 1806; but a lot about our hormones has changed in over 200 years!
Newer studies show that almost 1/3 of women begin their cycles when it is a new moon.
The moon will affect us in many physiologic ways, not just our menstrual cycle. For instance we sleep, on average, an hour shorter per night during the full moon!