Everyone knows there can be two full Moons in a month. Is it possible to have no full Moon in a February containing 28 days?
Yes, but only about four times in a century. This happened in 1999 and will next occur in 2018, assuming the phases are expressed in Universal Time. When February has no full Moon, January and March typically have two full Moons each (the second being widely hailed as a blue Moon). Much rarer is a 29-day February (in a leap year) with no full Moon. According to Peter Macdonald (Journal of the British Astronomical Association, December 1998, page 324), this oddity occurred in 1608 and won’t happen again until 2572.
— Roger W. Sinnott