There isn’t an even number of days in a lunar month nor even in a year. We just say there is. Phases of the moon last about 29½ days, so 12 of them add up to 354 days, but a year lasts about 365¼ days. This is the crux of the problem. Each culture in different ways approximates the year with months of different lengths because we accept the daily cycle and like to count in days even though the solar day is not the same number of seconds throughout the year.
Book of Months