Requiring First & Last Month for Month-to-Month Rental Agreement (CA)

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My own current month-to-month rental agreements I propose are pretty simple (KIS is my philosophy when it comes to paperwork, etc) and require minumum 30 days advance notice from either party of vacating unit. Same in my own 6 month agreement I propose, except I do require first and last months rent paid at lease signing.

I've seen lots of area PMs and landlords require both first and last plus a month of deposit, equaling 3X rent down at signing of even 1 and 2 year minimum residential rentals, but have never entertained going that far.. yet. This is a rather upscale city in the county though, and I have noticed these requirements do tend to attract a more financially stable tenant as far as savings at the moment of looking to move, for clients I have been PMing for.

Anyways what I'd like to know is if for a month-to-month agreement in CA (LA county) can I legally also start requiring first and last months rent prepaid? 

Both lawyers' and laypersons' insight would be appreciated, thanks! =D