L.A. County’s unemployment rate dipped slightly last month to 4.5 percent, the combined effect of a modest gain in jobs and several thousand workers leaving the labor force. The state Employment Development Department reported June 21 that the unemployment rate for Los Angeles County fell from a revised 4.6 percent in April. The rate has generally hovered between 4.6 percent and 4.7 percent for much of the past year, indicating an economy near full employment. The county’s 4.5 percent unemployment rate remained higher than the statewide average of 4.2 percent and the national average of 3.6 percent. The unemployment rate, which is based on a monthly household survey, dropped in large part because the county’s labor force shrank in May by about 14,000 to 5.11 million. That has run counter to national trends that have seen more people entering the labor force in search of higher-paying jobs. The payroll job count in Los Angeles County rose by 8,000 in May to 4.56 million, led by a gain of 9,400 jobs in the leisure and hospitality sector in anticipation of the summer tourism and live entertainment season. Other industries posting slight job gains were employment services (up a net 4,600 jobs), construction (up 2,200 jobs) and government (up 1,100 jobs). The entertainment sector posted the largest net decline of 5,500 payroll jobs, while educational and health services dropped by a net 2,500 jobs as the academic year wound down.