OK, the answer is simply how many years it takes for m lunar cycles of length 29.53059 days to equal 365.2422 days to get a reoccurance accuracy of 0.01 days of 15 minutes. A simple computer program can be written to determine the commensurability time for any degree of precision. To get within an hour, my calculator says in 19 years you have 235 lunar months with an accuracy of 0.15 days or 3.6 hours. This is, of course, the well-known lunar Metonic Cycle. To get even closer in time, you have to wait 353 years for lunar month 4366 when the difference is only 0.064 days or 92.1 minutes since 4366 x 29.53059 days = 128,930.5559 days = 353x365.2422 = 128,930.4966 days. Below are the lunar month numbers, the year and the difference for higher precision reoccurances:
Month ( Lunation) Elapsed year day error minutes ........................................................................ 4366 353 0.064 92.1 8497 687 0.040 57.6 46146 3731 0.0072 10.3 62905 5086 0.0019 2.7 ........................................................................By the time you get to 600 years hence, roundoff errors and the details of the lunar orbit become important, and the above simple method breaks down. The point is that you have to wait more than a human lifetime for the Moon to re-occur in ANY phase within a few hours of the exact date and time of its last observation.