L.A. County’s unemployment rate was unchanged in May at 7.6 percent amid modest job gains that left the county just short of its all-time payroll jobs peak, state figures released Friday show.

The unemployment rate has held steady since March as more county residents both entered the workforce and found work, according to data from the California Employment Development Department. The rate is down from 8.3 percent in May of last year and is now at the lowest level since June 2008.

That good news is relative, however, as L.A. County unemployment levels still exceed the statewide rate of 6.4 percent and are more than two points above the national rate of 5.5 percent. Unemployment in the county’s two largest cities was slightly higher than the countywide rate, with Los Angeles at 7.8 percent and Long Beach at 8 percent.

The state figures show the county, which has slightly more than 4.3 million nonfarm jobs, gained just 3,600 payroll jobs in May. The total is now just 2,700 jobs shy of the all-time high reached in December and is 19,000 jobs above the previous peak of December 2007.

The modest job gains in May were spread around a number of industries, led by increases in health care/social assistance (up 6,800) and accommodation/food services (up 3,400). Government, construction, retail trade and transportation/warehousing also recorded slight gains.

The often volatile entertainment sector lost the most payroll positions in May, shedding nearly 12,000 jobs.

In the more closely watched year-over-year jobs figures, county payrolls swelled by 100,000 jobs over the last 12 months for a robust annual growth rate of 2.4 percent.

Virtually all sectors reported strong year-over-year job gains, led by health care/social assistance (up 21,400 jobs), leisure/hospitality (up 16,000), government (up 12,000) and professional/business services (up 10,000).

Only manufacturing didn’t join the party, with the sector shedding 2,100 jobs.