The most recent incident came late Sunday afternoon, when officers responded to a report of a man armed with a gun near Ascot Elementary School, LAPD Sgt. James Townsend said.
Police made contact with the suspect, described only as a Hispanic male, and an officer-involved shooting occurred, Townsend said.
No other details about what led up to the shooting were released.
The shooting came about 28 hours after another fatal, police-involved shooting in the city.
Around 1 p.m. Saturday, officers tried to pull over a car with paper license plates, LAPD said. Officers suspected the vehicle, which had at least two people inside, was stolen.
But the car didn't stop, and officers gave chase, police said.
When the car finally did stop, two men ran away in different directions, the LAPD said. Two officers chased one of the suspects, following him to the back of a nearby home.
An officer fatally shot the man, less than two blocks away from where the foot pursuit started. Paramedics declared the man dead at the scene of the shooting. The officer's name has not been released.
No officers were injured and a handgun was recovered at the scene, the LAPD said. It was not clear Sunday what happened to the other man who fled the car.
Several CNN affiliates and the Los Angeles Times identified the man killed by police as Carnell Snell Jr., 18. His mother, Monique Morgan, was visibly distraught as she told reporters her son was shot five times.
"My daughter got a phone call," she said as she wept. "It said that the police shot him."
When speaking with CNN affiliate KABC, Morgan claimed Los Angeles police had not given her any information about her son.
"[The police] won't let me see him," Morgan told reporters. "They said they moved him already. I want to see him."
As with any officer-involved shooting, LAPD's Force Investigation Division will investigate and present its findings to Police Chief Charlie Beck. The chief, along with the LAPD board of commissioners, will determine whether the officer complied with the department procedures.
The Los Angeles District Attorney's Office also plans to review evidence collected during the investigation.
Crowds gathered near the scene of the Saturday shooting and remained there into the evening, but the demonstrations were peaceful. Police monitoring the protest initially wore riot gear, but removed it later, according to CNN affiliate KTLA.
The Los Angeles incidents follow recent police shootings of black men in El Cajon, California; Tulsa, Oklahoma; and Charlotte, North Carolina. The shooting victims in El Cajon and Tulsa were unarmed, but questions remain on whether the victim in Charlotte had a weapon.