Did the Book of Mormon Prophets Use the Mayan Calendar?

One of the ways in which Latter-day Saint apologists seek to defend the antiquity of the Book of Mormon is to argue that the Book of Mormon exemplifies elements of ancient Mesoamerican culture. An example of this strategy is the claim that the Book of Mormon’s references to periods of “four hundred years” and “five years” by a first-century BC prophet called Samuel the Lamanite (Helaman 13:5; 14:2) correlate with specific calendrical periods of importance in the ancient Mayan calendar.