Final answer:
The Aztecs believed the calendar would cycle every 52 years, which was marked by the New Fire Ceremony for renewal. The Maya Great Cycle lasted approximately 5,125 years, with the recent cycle beginning in 2012, which was often misconstrued as an apocalypse prediction.
Step-by-step explanation:
The Aztecs, along with other Mesoamerican groups like the Maya, followed a sophisticated calendar system with interlocking cycles. One such cycle is the 52-year calendar round, after which they believed a period of renewal took place, marked by ceremonies such as the New Fire Ceremony.
On a much larger scale, the Maya Long Count Calendar measures time in terms of Great Cycles, each lasting approximately 5,125 years, with the most recent cycle beginning in 2012.
This date was misinterpreted by some modern individuals as predicting an apocalypse, but in reality, it was simply the start of a new cycle and likely would have been celebrated with major festivities by the Maya.