In 2016, the summer solstice will coincide with a full moon. How often does this happen? I found that the solstices work on a 400 year cycle based on this. I can't find anything similar for the lunar cycle. Is there a formula I can use to calculate the date of the full moon?
Florin Andrei what evidence can you supply to charge the oldest scientific body on this planet (The Royal Society at Greenwich) to be a profit-driven media entity.

Bishop, if you are asking when the 2 specific points in time match, it is true that they have a 'astronomical' infrequency to look at. But if you look at what the common terms for the definition of a solstice and full moon occurring at the same time, then it is not too infrequent. Matching a 24 hour period (solstice day) against a 72 hour period (a full moon) then they occur with a much more reasonable frequency. There are lots of lunar cycle calculators around. The current cycle we are in has the same middle day of the full moon  period In 2004, 2007, 2015, 2026, 2034, 2042 and 2045. further dates can be found using this http://aa.usno.navy.mil.
Just chose any date, calculate the drift on your 400 year cycle then calculate how often that drift occurs at the same time as the 3 day phase of the full moon drift. There will be large periods when the match occurs rarely (The center point of each phase occurring furthest apart). As the centre points close on each other the Frequency will increase. The recurring pattern of all astronomic movements.