If you have one machine downloading and installing the packages, you could use rsync or some other utility to copy them to your other ones (provided they're on the network). apt-get looks for the downloaded packages in /var/cache/apt/archives so that's where you'd copy them from and to. Then when you run 'apt-get dist-upgrade' it won't have to download the files from any remote server again.
Or configure the other machines to use your "host" machine as a repository.
See Google search results: mint set up local repo