Question

There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in same direction. After how many minutes will they meet again at the starting point?? ​

Answer 1

Answer:

hcm of 18 and 12=6 minutes is the correct answer

Answer 2

Answer:

Answer:

$\begin{tabular}{r|l}2&18 \\\cline{1-2}3&9\\\cline{1-2}3&3\\\cline{1-2}&1\\\end{tabular} \qquad \begin{tabular}{r|l}2&12 \\\cline{1-2}2&6\\\cline{1-2}3&3\\\cline{1-2}&1\\\end{tabular}$

18 = 2 × 3 × 3 × 1

⠀ = 2 × 3² × 1

⠀

12 = 2 × 2 × 3 × 1

⠀ = 2² × 3 × 1

⠀

• According to the Question :

They'll again meet after the Least Common Multiple of the time they both take to complete one round.

⠀⠀⠀⠀Understand it like One had already travelled 12 minutes and another is 18 minutes ahead. Now Both will meet when that Least Common Multiple of Both Time Happens.

We always take Highest Power of any of Multiple while we doing LCM.

⠀

$:\implies\sf LCM(18,12) = 2^2\times 3^2\times1\\\\\\:\implies\sf LCM(18,12) = 4\times9\times1\\\\\\:\implies\underline{\boxed{\sf LCM(18,12) = 36\:minutes}}$

⠀

∴ Both will meet after 36 minutes.