Question

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?​

Answer 1

Question:-

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?

Required Answer:-

Given,

$\sf{\rightarrow{ A \: completes \: a \: round \: in \: 252 \: seconds }}$

$\sf{\rightarrow{B \: completes \: the \: round \: in \: 308 \: seconds}}$

$\sf{\rightarrow{C \: completes \: the \: round \: in \: 198 \: seconds.}}$

To Find:-

$\sf{\rightarrow{The \: time \: they \: will \: meet \: again \: at \: the \: starting \: point?}}$

Solution:-

A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds.

They will meet again after the L.C.M. of 252, 308 and 198.

Now,

The prime factors of 252,308 and 198:-

$\sf{\bold{252} = 2 \times 2 \times 3 \times 3 \times 7}$

$\sf{\bold{308} = 2 \times 2 \times 7 \times 11}$

$\sf{\bold{198 }= 2 \times 3 \times 3 \times 11}$

Hence, the L.C.M.=

$\sf{2 \times 2 \times 3 \times 3 \times 7 \times 11 = \orange{2772}}$

Therefore, They will meet after 2772 seconds = 46 minutes 12 seconds.