The moon's elliptical orbit precesseses about once in just under 9 years. It is caused by the solar tide.
This precession period is equal to the time that number of sidereal months counted exceeds the number of anomalistic months counted by exactly one. This happens after about 3233 days.
This precession causes the full moon cycle to be over a month longer than a sidereal year.
There are approximately two lunar precession cycles in a saros cycle.