The county reported 2,901 new cases Monday, 4,108 cases Sunday and 5,685 on Saturday, raising the cumulative total from throughout the pandemic to 2,974,197.
The daily rate of people testing positive for the virus was 3.7% as of Monday.
County health officials were urging residents to mark Memorial Day with caution to prevent the spread of COVID-19.
"As we celebrate Memorial Day ... I'd like to extend my gratitude to all of our armed forces members and their families who have dedicated their lives to protecting us through their military service," county Public Health Director Barbara Ferrer said in a statement issued Friday.
"Many of us will attend events or host gatherings honoring these courageous men and women this long weekend," she continued. "Regardless of how you plan to spend the holiday, we ask that you reduce the chance of getting or spreading COVID-19 by taking advantage of four powerful tools -- vaccinations, masking, testing, and therapeutics."
Health officials have noted that many COVID-positive patients were admitted to hospitals for reasons other than the virus. But Ferrer said Thursday those patients still require advanced levels of care that put added stress on hospitals.
"They require a lot of different resources that are of higher intensity, so that in and of itself is more strain on the system," she said.
Ferrer announced Thursday that increasing case numbers across the county have led to a rise in virus outbreaks at skilled nursing facilities, prompting some tighter infection-control measures.
Staff at nursing facilities are now required to wear N95-level masks at all times and undergo twice-weekly testing, while residents must undergo weekly testing. All communal dining has also been halted, and all non-essential indoor group activities are being paused.
Los Angeles County remains in the U.S. Centers for Disease Control and Prevention's "medium" category of virus activity. Under CDC guidelines, counties in the "medium" category will move to "high" if the rate of new virus-related hospital admissions reaches 10 per 100,000 residents, or if 10% of the county's staffed hospital beds are occupied by COVID-positive patients.