Toy train A crosses a pole after every 24 seconds. Toy train B crosses the pole after every 30 seconds and toy train C crosses the pole after every 36 seconds. After how many minutes, do they all cross the pole together?

 Given : 

Train A crosses pole after every 24 seconds.

Train B crosses pole after every 30 seconds.

Train C crosses pole after every 36 seconds.

To find : 

We have to find after how many minutes they cross the pole together.

Solution :

Three trains crosses the pole after every 24 , 30 , 36 seconds respectively. They cross the pole together after common multiples of 24, 30 and 36.

We have to find the Least Common Multiple of 24 , 30 , 36 .

Factors of 24 = $2\times2\times2\times3$

Factors of 30 = $2\times3\times5$

Factors of 36 = $2\times2\times3\times3$

LCM = $2^{3}\times3^{2}\times5$

LCM = $8\times9\times5$ = 360

LCM  of 24 , 30 , 36  =  360

Convert 360 seconds to minutes

60 seconds = 1 minute

360 seconds = $6\times60$ seconds

$6\times60$ seconds = $6\times1$ minute = 6 minutes

360 seconds = 6 minutes

Therefore,

After 6 minutes the three trains cross the pole together.

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Updated on: 10-Oct-2022

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