They haven't won any Stanley cups, they made it to the finals once but were swept by the Detroit Red Wings in the 1997-1998 season
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Ken Dryden won 6 Stanley Cups in a career that only spanned 8 years.
they have been to only one Stanley cup
8: 1968, 1969, 1970, 1971, 1972, 1973, 1974, 1975
This depends on which cup and which Kings. The LA Kings have won 0 Stanley Cups thus far, although they have made it to the 2012 Stanley Cup Finals.
1998. The Detroit Red Wings swept the the Washington Capitals to win the 1998 Stanley Cup.