Depends heavily on how you have configured Apache. If you are using something like PHP and the forking model (most common MPM configuration), you can only handle as many requests as you have workers; additionally you are spinning up a full PHP interpreter when serving static assets. In my experience[1], putting Nginx in front of Apache to serve static assets and leaving Apache as a sort of application server is one of the lowest hanging fruit in scaling a LAMP application.

[1] Was Co-Founder/CTO of a medium-sized PHP PaaS company