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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 6 Months Ended
Feb. 28, 2023
Nov. 30, 2022
Feb. 28, 2022
Nov. 30, 2021
Feb. 28, 2023
Feb. 28, 2022
Earnings Per Share [Abstract]            
Net income $ 83.2 $ 74.9 $ 75.3 $ 87.6 $ 158.1 $ 162.9
Basic weighted average shares outstanding (in shares) [1] 32,048   34,964   32,178 35,007
Common stock equivalents (in shares) 338   400   367 437
Diluted weighted average shares outstanding (in shares) [1] 32,386   35,364   32,545 35,444
Basic earnings per share (in dollars per share) [1] $ 2.60   $ 2.16   $ 4.91 $ 4.65
Diluted earnings per share (in dollars per share) [1] $ 2.57   $ 2.13   $ 4.86 $ 4.60
[1] Earnings per share is calculated using unrounded numbers. Amounts in the table may not recalculate exactly due to rounding.