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Earnings Per Share - Basic and Diluted Earnings Per Share, Treasury Stock Method (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
3 Months Ended 9 Months Ended
May 31, 2023
Feb. 28, 2023
Nov. 30, 2022
May 31, 2022
Feb. 28, 2022
Nov. 30, 2021
May 31, 2023
May 31, 2022
Earnings Per Share [Abstract]                
Net income $ 105.0 $ 83.2 $ 74.9 $ 105.7 $ 75.3 $ 87.6 $ 263.1 $ 268.6
Basic weighted average shares outstanding (in shares) [1] 31,682     34,079     32,006 34,659
Common stock equivalents (in shares) 329     361     354 408
Diluted weighted average shares outstanding (in shares) [1] 32,011     34,440     32,360 35,067
Basic earnings per share (in dollars per share) [1] $ 3.31     $ 3.10     $ 8.22 $ 7.75
Diluted earnings per share (in dollars per share) [1] $ 3.28     $ 3.07     $ 8.13 $ 7.66
[1] Earnings per share is calculated using unrounded numbers. Amounts in the table may not recalculate exactly due to rounding.