Common meeting time around a track: A, B, and C complete one round in 252 s, 308 s, and 198 s respectively. Starting together from the same point, after how long will all three next be together at the start point?

Introduction / Context:
When multiple persons move in loops and we want their next simultaneous meeting at the start point, we compute the least common multiple (LCM) of their individual round times.

Given Data / Assumptions:

• T_A = 252 s
• T_B = 308 s
• T_C = 198 s

Concept / Approach:
Next simultaneous return to start occurs at LCM(T_A, T_B, T_C). Convert the result to minutes and seconds.

Step-by-Step Solution:

Verification / Alternative check:
Prime-factorize each time and take the maximum powers to confirm LCM = 2772 s.

Why Other Options Are Wrong:
Other durations are not multiples of all three given times.

Common Pitfalls:
Using GCD or pairwise meetings instead of LCM for all three together at the start point.

Final Answer:
46 minutes 12 seconds