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There are five hobby clubs in a college - photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meet on the same day within 180 days?

There are five hobby clubs in a college - photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meet on the same day within 180 days? Correct Answer 3

Meeting cycle of different groups:
Gardening = 2 days
Electronics = 3 days
Chess = 4 days
Yachting = 5 days
Photography = 6 days
They all will meet on the first day.
Number of days after they will meet again = LCM (2, 3, 4, 5, 6) = 60 days.
They will meet on the 1st day, 61st day and 121st day.

Hence, they will meet 3 times within 180 days.

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