Question

there is a circular park 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 start at the same point and at the same time and go in the same direction.after how many minutes will they meet at the starting point​

Answer 1

AnsweR                    ; 36

Step-by-step explanation:

Required number of minutes is the L.C.M of 18 and 12.

We have  

LCM is    

Product of the greatest power of each prime factor involved in the numbers.

      L.C.M of 18 and 12 =  

Hence Sonia and Ravi will meet after 36 min.

Answer 2

Given

Sonia takes 18 minutes to drive one round of the field.

On the other hand Ravi takes 12 minutes for the same.

To Find

After how many minutes will they meet at the starting point.

$\rule{200}2$

Solution

To find that after how much time they will meet at the starting point, we have to find LCM.

By Prime factorization method..

$\begin{array}{r|l} 2 & 18 \\ \cline{2-2} 3 & 9 \\ \cline{2-2} 3 & 3 \\ \cline{2-2} & 1 \end{array}$

Prime Factorization of 18 = 2 × 3 × 3

= 2¹ × 3²

$\begin{array}{r|l} 2 & 12 \\ \cline{2-2} 2 & 6 \\ \cline{2-2} 3 & 3 \\ \cline{2-2} & 1 \end{array}$

Prime Factorization of 12 = 2 × 2 × 3

= 2² × 3¹

OR

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

LCM of 12 and 18 = 2 × 2 × 3 × 3 = 36 min

Therefore, after 36 minutes they both meet again.