Does an LLC have to be formed in the state I live in?

[Jack Calhoun]

I live in CA and have created a CA LLC. I own a 4plex in AZ and plan to buy more out-of-state properties. I am thinking about scrapping the CA LLC due to the high yearly ($800) annual tax amongst other things. Can I then create an LLC based in Arizona or any other state where I purchase properties, even though I live out of state?  I am trying to avoid the heavy costs associated with California LLC's.  I've heard that LLC's are not absolutely necessary, but I would feel better for tax and protection purposes to have all business monies separate from my personal monies.  Thank you.