Andrea Allred shows how to cycle error logs to prevent them from growing out of hand:
What is a good size? I usually try to get it to roll over around 10 MB. I use a monitoring tool and when the large error log alert is triggered, I have it run sp_cycle_errorlog for me so mine always stay a healthy size. You don’t need fancy tools to do this though. If you know about how fast your logs grow, you can set up a SQL Agent job to run it on a schedule to keep your logs healthy.
How many logs should I keep? This is completely up to you, but since I keep my logs so small, I try to keep 15 of them. Why so many? I do it so I can go back and see issues further back if needed. You can adjust the amount you keep by right clicking on SQL Server Logs in SSMS and selecting “Configure”
I’d personally prefer to keep more logs—at least 32-45 days worth—but that’s going to depend upon the environment.