Ram and Shyam go for morning walk daily. They run in a circular track in the park and take 180 seconds and 150 seconds respectively to complete one round. They start together at 6 am from the same point and in the same direction.

(i) How long would it take for them to meet again for the next time?

(ii) At what time willl they meet first time after they start?

(iii) Which concept has been used here?

(iv) Which values of Ram and Shyam have been depicted in this activity?

Answer:
Ram take 180 sec to complete one round 
Shayam take 150 sec to complete one round
And
Start together at 6 am

i ) To find how long it will take for them to meet again , we find L.C.M. of time taken by both person

2 | 150, 180
2| 75 , 90
3| 75,45
3| 25,15
5| 25,5
5|  5 ,1
 | 1 , 1
So, L.C.M.   = 2$\times$2 $\times$ 3 $\times$ 3$\times$5 $\times$ 5   = 900
SO they will meet again in 900 sec or  in 15 min      ( Ans )

ii ) As they start running at 6 am , and meet again in next 15 min so,
The when they meet = 6:00 + 0:15 
= 6:15 am                                                                ( Ans )

iii ) we use Lowest common multiple method to solve this question , As we want to find when they meet next time ( lowest ),
And as they meet ( common )  and both are at same point ( multiple )

iv ) We can see that ram can run in 15 minutes total round of park = $\frac{900}{180}$ = 5 round
And
Shayam can complete total round of track in next 15 minutes = $\frac{900}{150}$ = 6 round
So in this activity we can say that in next 15 minutes when they meet again Ram completes 5 round and shayam complete 6 round of the circular track.