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Earnings Per Share (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
 3 Months Ended 9 Months Ended
May 31, 2024
Feb. 29, 2024
Nov. 30, 2023
May 31, 2023
Feb. 28, 2023
Nov. 30, 2022
May 31, 2024
May 31, 2023
Earnings Per Share [Abstract]                
Net income $ 113.9 $ 89.2 $ 100.6 $ 105.0 $ 83.2 $ 74.9 $ 303.7 $ 263.1
Basic weighted average shares outstanding (in shares) [1] 30,829     31,682     30,905 32,006
Common stock equivalents (in shares) 648     329     515 354
Diluted weighted average shares outstanding (in shares) [1] 31,477     32,011     31,420 32,360
Basic earnings per share (in dollars per share) [1] $ 3.70     $ 3.31     $ 9.83 $ 8.22
Diluted earnings per share (in dollars per share) [1] $ 3.62     $ 3.28     $ 9.67 $ 8.13
[1] Earnings per share is calculated using unrounded numbers. Amounts in the table may not recalculate exactly due to rounding.