"The Metonic cycle is the lunar cycle in question. After 19 years, the lunar phases are repeated on nearly the same calendar dates. It was discovered around 432 B.C. by the Greek astronomer Meton (although some believe that the Babylonians knew about it before he did). After 19 years, the lunar phases are usually repeated on the same calendar dates.
According to the cycle, a
full moon should have happened 19 years ago, in 1996, but it didn't
because the Metonic cycle is only approximate and the number of leap
days (four or five) in a period of 19 years can give rise to a
discrepancy of one day.
In 1996, the full moon fell not on Christmas Day, but Christmas Eve.
And in this particular case, adding 19 years to 1996 saw a jump of one
day, moving the full moon to Christmas Day in 2015.
Interestingly, if we use the Metonic cycle going backward from 1996, we
also jump forward one day to Christmas Day in 1977, which was the last
time we had a full moon on Christmas Day.
Now, if we add 19 years to 2015, we find that the Metonic cycle will work perfectly with no one-day jumps — so the next time a full moon will occur
on Christmas Day will be in 2034. But that will work only for the 48
contiguous states, because for those living in Alaska and Hawaii, the
moon will officially turn full before the stroke of midnight
on Christmas Eve.
Unfortunately, although I saw the moon last night, it's either too cloudy or too early to see it now.
Update: We went out later, saw the moon, and took a few photos. See you in 2034!