Question

Swapnil, Aakash and Vinay begin to jog around a circular stadium. They complete their revolutions in $36$ seconds $48$ seconds and $42$ seconds respectively. After how many seconds will they be together at the starting point?

• A. $504$ seconds
• B. $940$ seconds
• C. $1008$ seconds
• D. $470$ seconds

Answer 1

The correct option is C $1008$ seconds

They will meet at the time of which s equal to $LCM(36,48,42)$.

So, by using prime factorization method,

$36=2\times 2\times 3\times 3$

$48=2\times 2\times 2\times 2\times 3$

$42=2\times 3\times 7$

$\Rightarrow LCM(36,48,42)=2\times 2\times 2\times 2\times 3\times 3\times 7$

$=16\times 9\times 7$

$=1008$

Hence, at ${1008}^{th}$ second all three racers will meet together at the starting point.