Question

An ancient culture had a solar calendar with a 365 day cycle and a religious calendar with a 292 day cycle. If the calendars both start today, in how many days will they next coincide?

Answer 1

Make the Least common multiple (LCM) of 365 and 292:

$365, 292 | 5$
$73, 292 | 2$
$73, 146 | 2$
$73, 73 | 73$
$1, 1 |\underline{5*2*2*73 = 1460}$

Answer:
$\underline{1460\:days\:will\:they\:next\:coincide}$