Finishing job simultaneously

[neerajkumar1_1]

Sarah and Alice both work at an auto shop, where they are responsible for changing the oil in cars. It takes Sarah 12 minutes to do one oil change, while it takes Alice only 10 minutes. If there are lots of cars that need their oil changed, and Sarah and Alice both start doing oil changes at exactly 9:00 A.M., and start the next car as soon as they finish changing the oil in another car, what is the first possible time that they will finish changing the oil of a car simultaneously?

[spoiler]Answer: 10:00 am[/spoiler]

I dont have the options but i have mentioned the correct answer.
The problem seems slightly different and is not a regular T&W problem.
If someone could explain the logic and concept behind the problem.
Thanks

[student22]

Here's the way I solved it:

Sarah changes oil in multiples of 12
Alice changes oil in multiples of 10

You're being asked when they'll meet. Basically that's another way of asking what's the LCM (least common multiple) of the 2 numbers.

The least common multiple of 12 and 10 is 60.

So they'll meet 60 minutes from now or 10:00 am. Hope that makes sense.

[gmatjedi]

agree with the above post
key is recognizing the least common multiple

here's another way of demonstrating this:

sarah can change oil every 12 minutes, so she will complete a car at 12 min, 24, min, 36 min, 48 min, 60 min...
alice can change oil every 10 minutes, so she will complete a car at 10 min, 20 min, 30 min, 40 min, 50 min, 60 min...

therefore the answer is 60 minutes

by the least common multiple principle, you can also arrive at 60 minutes

[Scott@TargetTestPrep]

Sarah and Alice both work at an auto shop, where they are responsible for changing the oil in cars. It takes Sarah 12 minutes to do one oil change, while it takes Alice only 10 minutes. If there are lots of cars that need their oil changed, and Sarah and Alice both start doing oil changes at exactly 9:00 A.M., and start the next car as soon as they finish changing the oil in another car, what is the first possible time that they will finish changing the oil of a car simultaneously?

After starting together at 9:00 a.m., they will finish changing times simultaneously exactly after the least common multiple (LCM) of the number of minutes it takes for each of them to perform one oil change. Since 10 = 5 x 2 and 12 = 3 x 2 x 2, the LCM of 10 and 12 is 5 x 3 x 2 x 2 = 60. Therefore, they will finish together exactly 60 minutes after starting at 9:00 a.m., at which time it will be 10:00 a.m.