# I have a problem. A theater runs 2 movies The first movie is 40 minutes long, the second is 60 minutes long. They start at 3:00. At what time will they start at the same time again?

I know the answer is 5:00. I know it robably has something to do with 120 minutes somehow. I have not had algebra since high school 20 years ago and I do not know how to set up the problem.

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1. list the multiples of each movie's starting times from now

40 80 120 160 .. minutes
60 120 180 ...minutes

notice in 120 minutes from now, they both start.
And 120 minutes from 3:00 is 5:00

(no algebra needed)

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2. First, 5:00, 120 minutes, is right.

You can do this without algebra. In fact, algebra would only complicate it.

In the jargon, 120 is the lowest common multiple (LCM) of 40 and 60. That means that it's the smallest number that both divide into evenly.

40, 80, 120
60, 120

So 120 is the smallest number of minutes for both of the films to show completely in at the same time. The first shows 3 times; the second twice.

In fact, they will finish at the same time every two hours. 120 minutes, 240 minutes, 360 minutes - they all divide by both 40 and 60. 120 minutes is just the first.

Is that clear enough?

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3. Thank you both so much. I did figure it out using that method. I thought the teacher wanted algebra, but apparently she just needed to know if we could figure out a problem if given one. Check our skills so to speak. Again, thank you both so much.

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