Kenmore products are made by many different companies depending on the product. For example, Kenmore sewing machines are now and have been for several years made by Janome. These machines have the prefix 385 in their serial numbers. As for LG, I have no idea.
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LG manufactures the Kenmore Elite 29002 and 29272. Whirlpool manufactures the 21102, 21202, 21302, 26002, and 28002. LG manufactures all Kenmore/Kenmore Elite front-loaders except for the 49032, which is manufactured by Samsung.
GE, Kenmore, LG and Whirlpool all make steam washer/dryer combos.
Kenmore, LG, and Whirlpool top the list.
Some are. The first three numbers before the coma in the model number tell you who made your kenmore.
The best brands for refrigerators are LG, and Kenmore.
Gibson AKA Frigidaire
according to the sales people at Sears, the 31512 is manufactured by LG. Since there are LG's are that have many of the same features, they are probably right.
I was told by a veteran Sears representative that LG now makes all of the Kenmore refrigerators..