A, B, and C start at the same time in the same direction

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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 252s, B in 308s and C in 198s, all starting of the same point. After what time will they meet again at the string point ?

1. 26 min and 18s
2. 42 min and 36s
3. 45 min
4. 46 min and 12s

Correct Option: D

The time which all the three persons meet will be the LCM of the time 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 2772 i.e.,46 min and 12s.