It started at the Montair Apartments in the 8900 block of Grant Street just before 2 p.m.
Thornton Fire put the fire out and was mopping up hotspots about an hour later.
The fire started in a third-floor unit, but it is unclear how many units were damaged.
Firefighters say there were heavy flames and smoke when they arrived on scene.
No one was rescued, but some people were inside the building when the fire began and had to evacuate.
No injuries have been reported.
Some people were displaced by the fire, but authorities were not immediately sure how many.
The units do have smoke detectors, but they have not been checked.
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