About 1.4 million homes, or about 3.4 percent of all homes with a mortgage, were in the national foreclosure inventory as of May, according to CoreLogic.

That’s down from 1.5 million homes, or about 3.5 percent of all homes with a mortgage, a year earlier.

Over the past 12 months, there were more than 819,000 foreclosures completed nationwide, an average of 2,440 every day. Still, that’s down 27 percent from a peak of 1.1 million in 2010, CoreLogic said.

The top five states for completed foreclosures in the 12 months ending in May were California, Florida, Michigan, Texas and Georgia. Those states account for 48.8 percent of all foreclosures nationally.

The five states with the lowest foreclosure totals for the last year were South Dakota, Washington, D.C., North Dakota, West Virginia and Hawaii.

In Massachusetts, the foreclosure inventory was about 2 percent of all homes with a mortgage, or about 8,417 homes. That’s down about 0.1 percent from a year ago, CoreLogic said.