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?

Question

Accepted Answer

To determine when A, B, and C will meet again at the starting point, we calculate the Least Common Multiple (LCM) of their respective times to complete one round: 252 seconds, 308 seconds, and 198 seconds.

### Steps:

**LCM Calculation:**  
   The LCM of 252, 308, and 198 is calculated using the formula:  
   $$
   	ext{LCM}(a, b) = \frac{a 	imes b}{	ext{GCD}(a, b)}
   $$  
   Applying this iteratively for the three numbers gives:  
   $$
   	ext{LCM}(252, 308, 198) = 2772 	ext{ seconds.}
   $$

**Convert Seconds to Minutes and Seconds:**  
   Divide 2772 seconds by 60 to convert into minutes:  
   - Minutes: $$2772 \div 60 = 46$$  
   - Remaining Seconds: $$2772 \mod 60 = 12$$

### Final Answer:  
A, B, and C will meet again at the starting point after **2772 seconds**, which is equivalent to **46 minutes and 12 seconds**.

Answer

Answer

Answer