CHICAGO, May 4 (Reuters) - Chicago Mercantile Exchange lean hog futures hit contract highs for the third consecutive day on Tuesday as a strong cash market and tight supplies pushed up prices.

Solid demand for pork has helped boost the market, with meat processors paying up to buy hogs from producers, analysts said.

The U.S. Department of Agriculture pork cutout value has climbed recently, reflecting the demand. The cutout slipped by $0.48 to $111.18 per cwt for carcasses on Tuesday, though.

Hog supplies remain limited, in contrast to ample supplies of cattle available in the market, said Rich Nelson, chief market strategist for Illinois-based broker Allendale.

"The hog side now has a shortening supply of hog numbers," he said.

CME most-active June lean hogs set a new contract high of 113.800 cents per pound before trimming gains to settle up 0.9 cent at 113.550 cents per pound. The contract has gained 37% this year.

July hogs set a contract high for the third consecutive day, topping out at 113.650 cents per pound before ending at 113.425 cents.

Meatpackers are slaughtering a steady number of hogs at a time of year when the pace of slaughter would normally be declining, Nelson said.

Packers processed an estimated 487,000 hogs, compared to 486,000 hogs a week ago, according to the U.S. Department of Agriculture. They slaughtered 121,000 cattle, unchanged from a week earlier.

CME's June live cattle futures fell 2.275 cents to 113.025 cents per pound, while August feeder cattle futures sank 3.625 cents to 143.175 cents per pound.

Domestic and export demand for U.S. beef remains robust, traders said. The strong demand is helping to fuel a "significant disconnect" cash cattle and wholesale beef prices, Nelson said.

Choice beef cutouts jumped by $1.92 per cwt to $301.22, while select cuts rose $0.12 to $283.91, according to the USDA. (Reporting by Tom Polansek in Chicago; Editing by Sam Holmes)