What is the name of the cycle whereby the lunar azimuth and altitude recur on a given day? Like the Metonic cycle, except for position in the sky, not phase.

Original question: If I look up at the moon tonight, how long before it is in the same apparent position, and same phase, again?

I realized I can calculate this myself, if only I know two piece of information. Unfortunately I do not know the name of the second.

My question should be answered by the product of:


the Metonic cycle, and
the cycle where the moon's azimuth and altitude recur on a given day


What is the name of this second cycle?
You are looking for the Metonic cycle.  This is almost exactly 19 years, and represents 235 synodic months.

Now you have edited the detailed question so that it is out of sync with the original Title.  The other period you need is the Draconic month, which is the period between the moon crossing the ecliptic (in the same direction).