Kenmore is an American brand name known to many households for generations. The brand appeared just after electricity became common in most American households. The Kenmore name has always been seen in both catalogs and stores of Sears, Roebuck and Company. Here's some information on who makes Kenmore washing machines.
Kenmore is a brand first introduced in 1927. Kenmore washing machines are not made by any one single company, but are branded as "Kenmore" by five manufacturers.
Kenmore has always been a Sears brand. Sears has never manufactured any of their brands themselves, including Kenmore.
Most Kenmore washing machines are made by Whirlpool. Whirlpool also makes KitchenAid and Maytag appliances.
Frigidaire makes a lower-end front-load washer and dryer under the Kenmore name. Tappan and White Westinghouse are also machines made by Frigidaire.
While GE does make Kenmore products for Sears, it does not make the washing machines. GE is mainly the manufacturer of Kenmore ranges.