Metonic cycle

The Metonic cycle is a period of about 19 years used in astronomy and calendar studies. In particular, it is often used in the structure of lunisolar calendars, because 19 solar years is almost exactly the same length of time as 235 lunar months.
History.
The Metonic cycle is named for the astronomer Meton of Athens, who used the cycle in the calendar of Attica in the 5th century BCE. But it was used in the calendar of many ancient cultures, including Babylonia and China, before then.
Using the Metonic cycle in a calendar.
Nineteen years of 12 lunar months each would last a total of lunar months. But from astronomy we know that 19 solar years are the same length as lunar months. So over 19 years, extra lunar months need to be added to make the years line up correctly. Adding a thirteenth month in a year is called "intercalation." There are different ways to do it:
Metonic cycle and eclipses.
A Metonic cycle is close to the length of 20 eclipse years. For that reason, some eclipses repeat for a time at 19-year intervals.