Question

Two cyclists are riding along a circular path. The first cyclist completes the round in $12$ minutes, while the second cyclist completes the round in $18$ minutes. If they both started at the same pace and at the same time and are riding in the same direction, after how many minutes will they meet again at the starting point?

Answer 1

Let after $m$ rounds of first and $n$ rounds of second they meet

$12\times m=n\times 18$

$\therefore$ $\frac{m}{n}=\frac{3}{2}$

Taking $m=3$ we have

$time=3\times 12=36min$