QUESTION

CSAT

Hard

Maths

Prelims 2016

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?

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Explanation

To solve this, find the LCM of the meeting intervals: $2$ , $3$ , $4$ , $5$ , and $6$ .

LCM of $2$ , $3$ , $4$ , $5$ , and $6$ :

Prime factorization: $2 = 2$ $3 = 3$ $4 = 2^2$ $5 = 5$ $6 = 2 \times 3$ LCM $= 2^2 \times 3 \times 5 = 60$ .

How many times they meet in 180 days: Number of times = $180 / 60 = 3$ .

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