The district, with 688,000 students, faces a $718 million budget shortfall.
Layoff notices will go out by March 15 and the actual number to be laid off will be determined no later than June 30.
A raucous group of nearly 50 teachers and a few parents disrupted the board meeting. The group announced it was staging an act of civil disobedience and came prepared to be taken away in handcuffs. Some had previously volunteered to be arrested.
However, district officials made no move to carry out arrests and the group abandoned its effort.
"We got our message across. We made the best of it. We'll move on from here," said A.J. Duffy, president of United Teachers Los Angeles.
Teachers said layoffs will increase classroom sizes, get rid of some of the younger, more energetic teachers due to seniority rules, and eliminate innovative programs.
"As it is, it's a struggle to reach every one of my students," said Gilliam Russom, a history teacher at Roosevelt High School.
Los Angeles schools Superintendent Ramon Cortines said factors that will determine the actual number of layoffs in the district will include declining enrollment, the effectiveness of an early retirement incentive package being developed, state funding and the amount of money the district may receive from the federal economic stimulus.
"I am attempting to make sure that we have all options so that we do not face the issue of bankruptcy," he said.
The district has 36,000 teachers and 12,000 professional workers.
According to the California Teachers Association, about 14,000 teachers in the state received layoff notices last year, but fewer than half that number ended up losing their jobs.