LCM HCF L1

There are five 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 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?

  1. 5
  2. 3
  3. 18
  4. 10

Solution

All five hobby clubs will meet on the day that is multiple of 2, 3, 4, 5 and 6.

LCM of 2, 3, 4, 5 and 6 = 60.

All five groups will meet every 60th day. So, in 180 days, they will meet 3 times - 60th, 120th and 180th day.

The correct option is B.