Depends. Most landlords run a complete credit check and rental history (although many who just own a property or two don't). Sometimes the rental history can be the hold up because you have to wait for a reply, usually via fax or email, from past landlords. That is usually what takes the longest for me to approve an applicant. If a company or past landlord is willing to answer questions over the phone, it can take as little as 24 hours.