Apparently the HHOF recognizes these teams as dynasties:
Ottawa: 4 in 8 years (1920, 1921, 1923, 1927)
Toronto: 4 in 5 years (1947-49, 1951)
Detroit: 4 in 6 years (1950, 1952, 1954-55)
Montreal: 5 in 5 (1956-60)
Toronto: 4 in 6 (1962-64, 1967)
Montreal: 4 in 5 (1965-66, 1968-69)
Montreal: 4 in 4 (1976-79)
NY Islanders: 4 in 4 (1980-83)
Edmonton: 5 in 7 (1984-85, 1987-88, 1990)
4 seems the key number here. The Ottawa one is kind of weird as it goes 3 in 4 and then a 4th tacked on 4 years later. Every one of these has a back-to-back. The Toronto/Montreal one in the 60s does overlap but barely... Toronto's 67 title comes just puts a break in Montreal's 4 in 5 run, which started after Toronto had their own 3 straight run.
https://en.wikipedia.org/wiki/Dynasty_(sports)#National_Hockey_League
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