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A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet again at the starting point?

Correct answer: D. 46 min 12 sec

  • A. 26 min 18 sec
  • B. 42 min 36 sec
  • C. 45 min
  • D. 46 min 12 sec

Explanation

They return to the starting point together after the LCM of their lap times. 252 = 2^2 x 3^2 x 7, 308 = 2^2 x 7 x 11, and 198 = 2 x 3^2 x 11, so the LCM is 2^2 x 3^2 x 7 x 11 = 2772 seconds = 46 minutes 12 seconds. The likely mistake is using an ordinary sum or a smaller pairwise LCM instead of the LCM of all three times.

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