It was the Texas Rangers with a combined 30 runs to three against the Baltimore Orioles
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The most runs scored in one game by one team is 36 by the Chicago in 1897. For an AL team it's the Texas Rangers at 30 in 2007. For a combined score the most is 49 between Chicago (26) and Philadelphia (23) in 1922.
Hank Aaron had the most home runs for a regular season.
In MLB, that was 4 against the Philadelphia Athletics on June 3, 1932.
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Barry Bonds has the most home runs in Major League Baseball (762).