Actually it rotates once per sidereal period which is precisely 27 days 7 hours and 43.2 minutes. Shorter than any calendar month.

The synodic period is, the time it takes the moon to reappear at the same point in the sky is 29 days 12 hours and 44.0 minutes. Longer than any February and shorter than any other calendar month.

But you were reasonably close.

DA Morgan