There are 5 hobby clubs in a college viz. photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group 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 a year?
Explanation:
Gardening group meets once in 2 days, electronics group meets once in 3 days, chess group meets once in 4 days, yachting group meets once in 5 days and the photography group meets once in 6 days.
If they meet on the same day at one time, then the next time they will meet on same day again will be the LCM of 2, 3, 4, 5 and 6 which is equal to 60.
Hence, within 365 days all the five groups will meet on the same day = 365/60 = 6 times.
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By: Deepak Dawra