Does the Mountain Lion installer work on any Mac capable of running Mountain Lion or is it hardware specific?
Once you have downloaded it from the App Store, but before you run it, you can copy the Install Mountain Lion app into the Applications folder of any Mac you have an Admin account on (and have signed into the App store as you obviously) and run it from there.  If the Mac is not recent enough to install Mountain Lion the installer will tell you, otherwise it will happily install Mountain Lion for you.  That's how I updated all the Macs at my place.

Note that once run the installer will delete itself from the Applications folder.