Would this work?

[Finfan]

I'm building up a new ride and I was curious if I can use a Mountain bike 3 sprocket crank with a cruiser/coaster brake rear hub. I'm thinking I could use a front derailer to be able to shift gears while not having to do harsh things to the beach cruiser frame I'm using since a mountain bike rear wheel just doesn't fit properly. I'm concerned that the chain may not be compatible with the tooth dimensions between the different styles and that there may be problems I haven't considered. Thanks!

[Venice Motor Bikes]

The chains are a little different between coaster brake sprockets & derailleur sprockets!
Make sure they all work before swaping out all the parts!!