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How to change a water filter in a kenmore refrigerator 
Locate the manufacturer of the kenmore refrigerator, to find the model part number. 
You can find this in the refrigerator manual, or by doing some online research. 
Order your part online or by calling the number in the manual that is recommended for kenmore replacement filters.
A number of water filtration brands, like pur and brita may be available to you. Take the filter out of the box, and remove the caps on the end of the filter.