Docker Auto deploy containers to multiple hosts

Greetings everyone,

I have used docker before and now i am using it again cause i love docker’s simplicity. I currently am working in a Meteor (node react) environment.

The problem i am facing is, i have 6 different servers (hosted seperately) and 1 load balancers. The 6 different servers use the same container (Same source code). The hectic part is, everytime i deploy i am currently creating a build, deleting the running containers and creating a new container to all those 6 different server (there is a service called meteor-mup that those this ). This process takes around 30-40 minutes every time. And I am sure docker has a solution out there and i am just unable to start where to look for.

What i am looking for?
Let’s say i deploy to one of the container (lets say a master container), and this gets automatically replicated to the remaining 5 servers. I found something with docker swarm, am i heading in correct direction?

Any suggestion or help is much appreciated.