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How many years is the leap month a cycle in the history of China?
Every two to three years.

In the history of our country, before the Qin Dynasty, the leap month was placed at the end of a year, which was called "March". The leap month in the early Han dynasty was placed after September, which was called "post-September".

Since then, it has been stipulated that "the month without gas is the leap month of the previous month", which is still in use today.

Extended data:

In the China lunar calendar, a year with a leap month is called a leap month year. The general year is 12 months, 354 or 355 days, and the leap year is 13 months, 383 or 384 days.

As a kind of lunar calendar, the number of days in each month depends on the monthly loss, and the time of one year is based on 12 months.

In order to close the earth's cycle around the sun, that is, the tropic year, one month is added every two to four years, and the added month is a leap month, so the leap year of the lunar calendar is 13 months.

References:

Leap Moon-Baidu Encyclopedia