Question

A, $B$ and $C$ start to run around a circular stadium at the same time, in the same direction. A completes a round in $252$ seconds, $B$ in $308$ seconds and $C$ in $198$ seconds, all staring at the same point. After what time will they meet again at the starting point?

Answer 1

A completes his round in 252 secs.

B completes his round in 308 secs.

C completes his round in 198 secs.

They will again starting together

after,

LCM(252,308,198)

252=$2\times 2\times 3\times 3\times 7$

308$=2\times 2\times 7\times 11$

198=$2\times 3\times 3\times 11$

Required LCM = $2\times 2\times 3\times 3\times 7\times 11$= 2772 secs

60 secs = 1 min

2772 secs = $\frac{2772}{60}$= 46 mins 12 secs