Ouch, that sucks.
The one thing I can think of is to look up the Kenmore brand of washers and find the equivalent LG brand. LG makes the washers for Kenmore.
Then find that Kenmore part, it "should" be the same.
This is the part chart for Kenmore -
http://www.appliance411.com/parts/sears.shtml
Your best bet is probably finding the manuals for the Kenmore ones and see if they match yours and then order the part from Sears.