Job openings fell in June, suggesting that the labor market is cooling.

The number of job openings fell for the third consecutive month in June, a sign that the red-hot U.S. labor market may be starting to cool off.

Employers posted 10.7 million vacant positions on the last day of June, the Labor Department

. That is high by historical standards but represents a sharp drop from the 11.3 million openings in May and the record 11.9 million in March. It was the largest one-month decline in the two decades…