Tom and Harry are racing go-carts. Tom takes 2mins 8seconds to complete a lap while Harry takes 2minutes to complete a lap. They both start from the start line at the same time. when will they next cross the start line together? show all the workings.

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  after 32 minutes

Step-by-step explanation:

They will both cross the start line together after each has completed a number of full laps in the same time that the other has completed an integer number of full laps. That time will be the least common multiple (LCM) of their lap times, 128 seconds and 120 seconds.

The difference of these times (8 seconds) is also a divisor of both times, so that value is the greatest common divisor (GCD) of the two lap times. The LCM can be figured as ...

  LCM(120, 128) = 120×128/GCD(120, 128)

  LCM = 120×128/8 = 1920 . . . . . seconds

Converting this to minutes, we get ...

  (1920 s)/(60 s/min) = 32 min

They will next cross the start line together after 32 minutes.