Is it possible to replace a MTB crankset to a Roadbike crankset on an MTB frame?
Sure you can, but its not going to do a lot for your overall speed.

As long as the BB to crank interface is the same, you can put whatever crank on you like.  

Any older bike will have a square taper interface.  Newer bikes can have Octalink or something newer again.  You will require the same interface, and a crank puller to suit.

Another option is to change the chainrings for larger ones, but that can have issues with too-large a jump between chainrings.

You can also change the rear cassette for one with a smaller-small cog.  11 tooth is the common minimum size.

Downside of all this is that the bike is still about the same weight, and you're not putting in any more power.  So the bike's going to go about the same speed but you'll be pedaling fractionally slower.