How many cats per household is it permitted in Los Angeles?
There's no legal limit. The more animals that need homes that you take in the better, just make sure that you've got the space, money, and ventilation to take care of however many you adopt.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
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While there may not be a "legal" limit, a landlord, homeowners' association, and the like may limit the number of pets allowed. The number may also be limited if the person keeping the animals is not keeping them properly or if there are sanitation issues. Contact animal control for further information: http://animalcare.lacounty.gov/default.asp