Why is the full moon sometimes 29 days and sometimes 30 days?

A lunar cycle is 29.53059 days. In order to make the number of days in a month an integer and synchronize with the Gregorian calendar, it is stipulated that a lunar month is 29 days, that is, a small month; About two months, there will be 1.05438+008 days, about one day. So add another month 1 day, which is 30 days in the big month. Otherwise, there will be a joke that "the first month is not dark and May is not round".