Question

Two bikers are riding a circular path. The first rider completes a round in 12 minutes. The second rider completes a round in 18 minutes. If they both started at the same place and time and go in the same direction, after how many minutes will they meet again at the starting point?

Answer 1

$$\begin{gathered} \mathrm{find}\mathrm{the}\mathrm{LCM}\mathrm{of}12\mathrm{and}18. \\ 12=2\times 2\times 3 \\ 18=2\times 3\times 3 \\ \mathrm{so},\mathrm{LCM}\left(12,18\right)=2\times 2\times 3\times 3 \\ =36. \\ \mathrm{Therefore},\mathrm{they}\mathrm{meet}\mathrm{after}36\mathrm{minutes}\mathrm{at}\mathrm{the}\mathrm{starting}\mathrm{point}. \end{gathered}$$