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 a pole after every 36 seconds. After how many minutes, do they all cross the pole together?

Given :

Ty trains A, B, and C crosses a pole after every 24, 30, and 36 seconds respectively.

To do :

We have to find, after how many minutes, do they all cross the pole together?

Solution :

The least common multiple of 24, 30, 36 is the required time after that all the rains cross the pole together.

LCM of 24, 30, 36

           2        |   24, 30, 36

                     |__________

           3        |    12, 15, 18

                      |__________

         2          |    4, 5, 6

                      |__________

                          2, 5, 3

       LCM $= 2 \times 2 \times 2 \times 3 \times 3 \times 5$

              $ = 2^3 \times 3^2 \times 5$

               $ = 8 \times 9 \times 5$

    LCM  $ = 360$    

$1 second = \frac{1}{60} minutes$

$360 seconds = \frac{360}{60} minutes  = 6 minutes$

Therefore, after 6 minutes three trains cross the pole together. 

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Updated on: 10-Oct-2022

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