Question

Maggie, Kate and Sam start running around a circular track together and complete one revolution in $2,4$ and $6$ hours respectively. After how many hours will they all meet again?

• A. $6$
• B. $12$
• C. $8$
• D. $24$

Answer 1

The correct option is B $12$

Given that Maggie takes $2$ hours, Kate takes $4$ hours and Sam takes $6$ hours to complete one revolution.

We need to find the LCM of $2,4$ and $6$ in order to find the time after which they all will meet.

$\begin{array}{cc}2& 246\\ 2& 123\\ 3& 113\\ & 111\end{array}$

$\therefore$ LCM $=2\times 2\times 3$
$=12$

Therefore, they all will meet again after $12$ hours.