Excluding the two end points (1901 & 2024), here are the biggest gaps between seasons selected...
Detroit Tigers: 40 years (1968, 2008)
Oakland Athletics: 39 years (1931, 1970)
Cleveland Indians: 37 years (1957, 1994)
San Francisco Giants: 28 years (1934, 1962)
Baltimore Orioles: 28 years (1933, 1961)
Cleveland Indians: 27 years (1922, 1949)
Philadelphia Philles: 27 years (1930, 1957)