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?
Answer & explanation
Answer: (d) 3
All five clubs meet together on days that are common multiples of 2, 3, 4, 5 and 6, that is every LCM = 60 days. Within 180 days that happens on days 60, 120 and 180 — three times.
- All five meet on a day that is a multiple of 2, 3, 4, 5 and 6.
- LCM(2, 3, 4, 5, 6) = 60.
- Within 180 days: days 60, 120 and 180 — 3 times.
Remember · Events repeating every a, b, c … days coincide every LCM(a, b, c …) days.
Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·