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Earnings Per Share (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
 3 Months Ended
Nov. 30, 2024
Nov. 30, 2023
Earnings Per Share [Abstract]    
Net income $ 106.7 $ 100.6
Basic weighted average shares outstanding (in shares) [1] 30,930 31,005
Common stock equivalents (in shares) 869 360
Diluted weighted average shares outstanding (in shares) [1] 31,799 31,365
Basic earnings per share (in dollars per share) [1] $ 3.45 $ 3.25
Diluted earnings per share (in dollars per share) [1] $ 3.35 $ 3.21
[1] Earnings per share is calculated using unrounded numbers. Amounts in the table may not recalculate exactly due to rounding.