Three runners A, B, and C start together from the same point around a circular track. Their lap times are A: 252 s, B: 308 s, and C: 198 s. After how much time will they next be together at the starting point?

Introduction: When several runners start together and repeat laps with different lap times, their next common meeting at the start occurs after a time equal to the least common multiple of their lap times.

Given Data / Assumptions:

• A lap: 252 s
• B lap: 308 s
• C lap: 198 s
• All start together at the same point

Concept / Approach: Compute LCM(252, 308, 198). Convert the resulting seconds to minutes and seconds for a readable time format.

Step-by-Step Solution:

Verification / Alternative check: Prime factorizations confirm that 2772 is divisible by 252, 308, and 198, and there is no smaller positive time that satisfies all three simultaneously.

Why Other Options Are Wrong: 26 min 18 s, 42 min 36 s, 45 min, and 44 min are not common multiples of all three lap times.

Common Pitfalls: Taking a simple sum or pairwise LCM instead of the LCM of all three values. Always combine all periods.

Final Answer: 46 min and 12 s