Question

Pls Help!
Ken and Hamid run around a track.
It takes Ken 80 seconds to complete a lap.
It takes Hamid 60 seconds to complete a lap.
Ken and Hamid start running at the same time from the start line.
How many laps will they each have to run when they next meet on the start line?
Ken = ?
Hamid = ?

Answer 1

$80 = {2}^{4} \times {5}^{1}$

$60 = {2}^{2} \times {3}^{1} \times {5}^{1}$

$lcm = {2}^{4} \times {3}^{1} \times {5}^{1}$

$\: \: \: \: \: \: = 240$

HENCE THEY BOTH WILL MEET AFTER 240 SECOND OR 4 MIN

KEN = 240/80 = 3ROUNDS

HAMID = 240/60 = 4ROUNDS

Answer 2

Ken will have to run 3 laps and Hamid will have to run 4 laps when they next meet on the start line

Solution:

Given that,

Ken 80 seconds to complete a lap

Hamid 60 seconds to complete a lap

How many laps will they each have to run when they next meet on the start line?

We need to find the least common multiple

LCM of 80 and 60

List all prime factors for each number.

Prime Factorization of 60 is:  2 x 2 x 3 x 5  

Prime Factorization of 80 is:  2 x 2 x 2 x 2 x 5  

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

2, 2, 2, 2, 3, 5

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 2 x 3 x 5 = 240

This means every 240 seconds they will both be at the start line

Since Ken completes a lap in 80 seconds, he completes:

$\frac{240}{80} = 3$

Ken completes 3 laps in 240 seconds

Since Hamid completes a lap in 60 seconds, he completes:

$\frac{240}{60} = 4$

Hamid completes 4 laps in 240 seconds

Ken will have to run 3 laps and Hamid will have to run 4 laps till they next meet on the start line

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