Name: Questions based on LCM and HCF
Uploaded: 2019-07-19
Duration: 27 min 33 s
Description: Watch this session to learn the approach to solve some very interesting questions based on HCF and LCM...

Question

John, Rishi and Feroz participated in track events. During practice sessions, their coach observed that John took

48 s e c o n d s

, Rishi took

72 s e c o n d s

and Feroz took

108 s e c o n d s

to run around a circular track. If they start running together at

6 a m

for half an hour, how many times will they all come together at a same position?

Accepted Answer

To find how many times John, Rishi, and Feroz will all come together at the same position on the circular track, we need to find the least common multiple (LCM) of the times it takes each of them to run around the track.

First, we can simplify the times by dividing each by their greatest common factor (GCF), which is $12 s e c o n d s$ :

John takes $\frac{48}{12} = 4$ laps to complete the track

Rishi takes $\frac{72}{12} = 6$ laps to complete the track

Feroz takes $\frac{108}{12} = 9$ laps to complete the track

Next, we can find the LCM of the number of laps each person runs.

The LCM of $4, 6,$ and $9$ is $36$ , which means that all three will be at the same position on the track every $36$ laps.

To determine how many times they will all come together in half an hour ( $30$ minutes), we need to find out how many $36$ -lap cycles they can complete in that time.

John completes $4$ laps in one cycle, which means he can complete $\frac{36}{4} = 9$ cycles in $30$ minutes.

Rishi completes $6$ laps in one cycle, which means he can complete $\frac{36}{6} = 6$ cycles in $30$ minutes.

Feroz completes $9$ laps in one cycle, which means he can complete $\frac{36}{9} = 4$ cycles in $30$ minutes.

The number of times they will all come together in half an hour is equal to the lowest number of cycles completed by any of them, which is $4$ .

Therefore, John, Rishi, and Feroz will all come together at the same position $4$ times in half an hour.

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