Employers in Los Angeles County added nearly 19,000 jobs in March, led by a rebound in local government services, according to state figures released Friday. The county’s unemployment rate remained unchanged from the prior month at 8.7 percent as more county residents re-entered the labor force looking for work. The rate is down from 10.1 percent a year ago, according to the figures from the state Employment Development Department. The largest cities in the greater Valley region showed modest drops in unemployment. Lancaster had the highest unemployment rate at 12.4 percent in March, down from 12.5 percent in February. Palmdale was second at 10.9 percent, down from 11 percent the previous month. Elsewhere, Glendale had 7.6 percent, down from 7.7 percent in February; Burbank reported 7.1 percent, down from 7.2; and Santa Clarita came in at 5.3 percent, an improvement over 5.4 percent in February. The largest city in the region, Los Angeles, reported unemployment of 9.7 percent in March compared to 9.8 percent the previous month. On the payroll front, employers added 18,900 jobs to bring the countywide total of just over 4.17 million. That’s just 26,000 jobs shy of the all-time payroll peak of 4.2 million jobs reached in early 1990. The county is more populous than it was nearly 25 years ago. The job gains were spread across a broad range of industries, led by the government sector. After years of sharp budget cutbacks, local governments added 5,000 jobs to their payrolls. Health and social assistance services, entertainment and construction also reported modest gains.