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Three men begin simultaneously to run along a circular track that measures 11 kilometers in circumference. Their speeds are 4 km/h, 5 km/h, and 8 km/h respectively. After how many hours will they all meet again at the starting point together?

Problems on L.C.M and H.C.F MCQs for PPSC, FPSC, NTS, and Pakistan government job tests. Select an option below, then read the explanation.

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Problems on L.C.M and H.C.Fmathematics-mcqs › problems-on-l-c-m-and-h-c-f
Published
12 Jul 2019
Last updated
28 May 2026

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Explanation

To find when they meet at the starting point simultaneously, calculate the time each takes to complete one lap: 11/4, 11/5, and 11/8 hours. The meeting time is the least common multiple (LCM) of these lap times. Multiplying each by 40 (the LCM of denominators 4, 5, and 8) gives 110, 88, and 55 respectively. The LCM of 110, 88, and 55 is 440. Dividing back by 40 results in 11 hours. Therefore, they will all meet again at the start after 11 hours.

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