There are five hobby clubs in the college: Photography, Yachting, Chess, Electronics, and Gardening. 1. The Gardening group meets every second day. 2. The Electronics group meets every third day. 3. The Chess group meets every fourth day. 4. The Yachting group meets every fifth day. 5. The Photography group meets every sixth day. How many times do all five groups meet on the same day within $180$ days?

QUESTION

CSAT

Easy

Reasoning

Prelims 2013

There are five hobby clubs in the college: Photography, Yachting, Chess, Electronics, and Gardening.

How many times do all five groups meet on the same day within $180$ days?

Select an option to attempt

Explanation

Step 1: Calculate the LCM of 2, 3, 4, 5, and 6.

Prime factorizations: $2 = 2$ $3 = 3$ $4 = 2^2$ $5 = 5$ $6 = 2 \times 3$ LCM is obtained by taking the highest powers of all prime factors:

Highest power of 2: $2^2$ Highest power of 3: $3$ Highest power of 5: $5$ Therefore, LCM = $2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60$

Step 2: Determine how many times they meet within 180 days. Divide 180 days by the LCM: $180 \div 60 = 3$

Conclusion: All five groups meet on the same day 3 times within 180 days. Therefore, the correct answer is:

A. 3

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