There have been people in the past who have tried using cloud solutions like Google Drive to keep their virtual machines in sync, but that would be the slowest and longest way of doing it. This is because Google Drive and many other free cloud storage services are not using Block-Level Synchronization. So what they will do is see a difference in files and re-download the entire virtual machine again, which will take time and resources.
The method I recommend is using software like GoodSync. This is free software that lets you keep big virtual machine files in sync at a much faster speed and less bandwidth. This method does work over both internet and local LAN. To read more about this method, read about it here. Basically, instead of just replacing the entire file, it looks at bytes and replaces only those changed bytes, thus making the entire process faster.
After you install GoodSync on the computer that will be your server, setup an account for the server and during setup select the GSTSP method of connection on the right and your local VM folder on the left. Now go to your computer you want to stay in sync with this "server" and setup another new account, then select the GSTSP path to the VM on the left, and your local folder on the right. Now both computers will have the VM files in sync!
When you add another computer do the same thing. Setup a new account, and select the GSTSP server and the new machine will stay in sync with it as well. Be sure to go to select the clock icon in the upper right corner and choose when to automatically back up the virtual machine files. I personally chose when I log off, but you can choose every hour if you want.