Me and my brother purchased a 1941 4-unit in Silver Lake (Los Angeles) back in 2003 for $560K (top of the market at the time, it needed major renovations, and we had to get rid of the existing tenants -- 3% down, 6.5% interest 30 year fixed). I lived in one unit and my brother lived in another and I estimated it would take 5 years for rents to catch up with our mortgage. We lived in it for 10-11years and rehabbed it for an estimate $150k-$200K over that time using cash from income. With renters in the two free units it took about 5 years before me and my bro could live rent free. We refinanced it in 2013 at 3.5% for another 30 years and it's fully rented. Now the property pays for itself and gives both of us a nice monthly income.
With the extra income I was able to buy a home in the nice part of Eagle Rock, which I'm slowly making renovations on and I can see leaving it and renting it out in 5 years as well.
For now, this works for me. But there's no fast cash in LA. It's slow and steady, but the rental income (if you can be patient) is worth it. Good luck!