Three athletes

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?

Correct answer:

t =  2772 s
t₂ =  46.2 min

Step-by-step explanation:

$$\begin{gathered} a=252\text{s} \\ b=308\text{s} \\ c=198\text{s} \\ 252=2^2\cdot 3^2\cdot 7 \\ 308=2^2\cdot 7\cdot 11 \\ 198=2\cdot 3^2\cdot 11 \\ LCM(252,308,198)=2^2\cdot 3^2\cdot 7\cdot 11=2772 \\ t=LCM(a,b,c)=LCM(252,308,198)=2772\text{s} \end{gathered}$$

$t_2=t\to \text{min}=t:60\text{min}=2772:60\text{min}=46.2\text{min}=46.2\text{min}$

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