There's a command line tool for running multiple commands on multiple Linux servers at once. Jack Wallen shows you how with Parallel-SSH.

Configuring PuTTY for SSH Connections Before initiating an SSH connection, you need to gather some vital information: the IP address or hostname of the Linux server you're connecting to, the port ...

It'll work pretty much the same under Mac as Linux. Give the ssh-keygen a blank password unless you want to use a ssh-agent to remember the password for you.