SSH login without password

Create key first with or without password .

avo@prod1:~> ssh-keygen -t rsa
Generating public/private rsa key pair.
Enter file in which to save the key (/home/a/.ssh/id_rsa): 
Created directory '/home/a/.ssh'.
Enter passphrase (empty for no passphrase): 
Enter same passphrase again: 
Your identification has been saved in /home/a/.ssh/id_rsa.
Your public key has been saved in /home/a/.ssh/id_rsa.pub.
The key fingerprint is:
3e:4f:05:79:3a:9f:96:7c:3b:ad:e9:58:37:bc:37:e4 avo@prod1.

Copy the key to all other machines on which you need to log in without password.

cat .ssh/id_rsa.pub | ssh avo@prod2 'cat >> .ssh/authorized_keys'

OR

cat .ssh/id_rsa.pub | ssh root@192.168.100.10 'cat >> .ssh/authorized_keys'

Or whatever your user and hosts are .