The above GIF shows a simplified Round-Robin load balancing method. In this load balancing method, the load balancer doesn’t care about the number of connections that are being handled by the server. The 1st connection is sent to the 1st server, 2nd connection to 2nd server and 3rd connection to 3rd server without any regard to the pre-existing connections.
The above GIF shows a simplified Least-Connections load balancing method. As the name suggests, the Load Balancer will send the connections to the server with the least number of connections.
In the initial state of the GIF, the servers, have 5,4,3 connections as noted. The 1st connection is sent to the server with the least number of connections – S3. The 2nd connection is sent to S2 as S1 has 5 and S2 & S3 are tied for number of connections at 4. The 3rd connection is sent to S3 as S1 & S2 have more number of connections (5) than S2 (4). In the last image, all the servers have equal number of connections at 5.