Try this beautiful Calendar Problem from PRMO 2016.
The date index of a date is defined as (12 × month number + day number). Three events each with a frequency of once in 21 days, 32 days and 9 days, respectively, occurred simultaneously for the first time on July 31, 1961 (Ireland joining the European Economic Community). Find the date index of the date when they occur simultaneously for the eleventh time.
LCM of numbers
Calendar
Number of months in a year
Excursion in mathematics
PRMO 2016 Problem 3
115
What is the LCM of 21, 32,9.
It is 2016
Observe that the event will occur in multiples of 2016 days.
Now 2016 is divisible by 12
Hence in a year There are 12 months. Hence they will occur on the same date and time but in a different year
