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Earnings Per Share - Basic and Diluted Earnings Per Share, Treasury Stock Method (Details) - USD ($)
$ / shares in Units, shares in Millions, $ in Millions
 3 Months Ended 9 Months Ended
May 31, 2022
Feb. 28, 2022
Nov. 30, 2021
May 31, 2021
Feb. 28, 2021
Nov. 30, 2020
May 31, 2022
May 31, 2021
Earnings Per Share [Abstract]                
Net income $ 105.7 $ 75.3 $ 87.6 $ 85.7 $ 62.9 $ 59.6 $ 268.6 $ 208.2
Basic weighted average shares outstanding (in shares) 34.1     35.7     34.7 36.5
Common stock equivalents (in shares) 0.3     0.5     0.4 0.3
Diluted weighted average shares outstanding (in shares) 34.4     36.2     35.1 36.8
Basic earnings per share (in dollars per share) $ 3.10     $ 2.40     $ 7.75 $ 5.70
Diluted earnings per share (in dollars per share) $ 3.07     $ 2.37     $ 7.66 $ 5.66