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

26 min and 18s
42 min and 36s
45 min
46 min and 12s

Correct Answer: 46 min and 12s

Explanation:

The time at which all the three persons meet will be the LCM of the time taken by each person individually to complete one round.
252 = 2² x 7¹ x 9¹
308 = 2² x 7¹ x 11¹
198 = 2¹ x 9¹ x 11¹
∴ LCM of 252, 308 and 198 = 2² x 7¹ x 9¹ x 11¹ = 2772
So, A, B and C will again meet at the starting point in 2772s i.e., 46 min and 12s

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