Three cyclists ride round a circular track, completing a lap in 252 s, 308 s and 198 s. They start together from the same point. After how many seconds are all three next together at the start?

Question

Accepted Answer

2772 s. 252 = 2^2 × 3^2 × 7, 308 = 2^2 × 7 × 11, 198 = 2 × 3^2 × 11. LCM takes the highest powers: 2^2 × 3^2 × 7 × 11 = 2772 s. (1386 forgets one factor 2; 5544 doubles it.)

Three cyclists ride round a circular track, completing a lap in 252 s, 308 s and 198 s. They start together from the same point. After how many seconds are all three next together at the start?

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