Mesoamerican civilisations ran two calendars at once. The tzolk'in among the Maya, the tonalpohualli among the Aztec, is a 260-day ritual count formed by pairing thirteen numbers with twenty named days. The haab', the xiuhpohualli among the Aztec, is a 365-day year of eighteen months of twenty days with five additional days at the end, regarded as dangerous and unlucky.
Any given day carries a name in both systems, and the pairing repeats only when both cycles return to their starting point together. That interval is the least common multiple of 260 and 365, which is 18,980 days: fifty-two haab' years, or seventy-three tzolk'in cycles. This is the Calendar Round, and 52 x 365 = 73 x 260 exactly, with no remainder and no correction required.
Fifty-two years is close to a long human life, which made the completion of a Calendar Round a generational event. The Aztec marked it with the New Fire ceremony, held at the hill of Huixachtlan: all fires in the city were extinguished, household goods were destroyed, and a new fire was kindled on the chest of a sacrificial victim at the moment the Pleiades passed the zenith, then carried outward to relight the hearths. The anxiety attached to it was explicit, there was no guarantee that the world would continue.
The system was used across Mesoamerica, by Maya, Aztec, Zapotec and Mixtec, with roots reaching back well before the Classic period. It is often described as Mayan alone, which is wrong. The 260-day count in particular is older than any of the civilisations that inherited it, and its origin remains unresolved.