Do I need to leave Beijing if I am there with a L visa valid for 6 months with multiple entries??

Yes, you need to leave Beijing when the stay duration per entry is up. For example, your 6 months multiple entry visa only permits you to stay in China for 30 days after entry, you have to leave Beijing when you have stayed in China for 30 days. If you don't want to leave China, you can apply for visa extension at the Exit-Entry Administrative Department of Beijing Public Security Bureau, however, once you get a new visa for another 30 days stay in Beijing, your multiple entry visa expires automatically.