How does a DigitalOcean Load Balancer keep databases in sync?

Say I have a Wordpress blog that is getting so much traffic. So much so, that my Apache server cannot keep up with the requests. To mitigate these timeouts due to large numbers of requests, I look at a DigitalOcean load balancer.

What I would like clarification on, is if I have 3x $10 droplets of the same setup, and 1x Digitalocean load balancer distributing the traffic between the 3, - if I simply go to my website and write a blog, presumably my requests are handled by 1 of the 3 servers , my question is this: how does DigitalOcean’s load balancers ensure that the MySQL databases holding Wordpress post and user data, keep everything in sync?

If I write a post or create a new user on “LON1-001” server , does the loadbalancer update “LON1-002” and “LON1-003” servers? Apologies but I am new to load balancing.

Thanks