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Share-Based Compensation - Narrative (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Pre-tax share-based compensation expense $ 88.3 $ 68.1 $ 51.7  
Income tax benefit related to share-based compensation expense 14.9 $ 11.2 $ 8.6  
Unrecognized compensation cost related to share-based compensation awards, net of estimated forfeitures $ 106.5      
Weighted average period for recognition of total unrecognized compensation cost 1 year 8 months 12 days      
Stock options        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Expiration period 10 years      
Vesting period 3 years      
Per share weighted average fair value of stock options granted (in dollars per share) $ 77.62 $ 87.68 $ 55.50  
Total intrinsic value of stock options exercised $ 69.8 $ 52.8 $ 108.4  
Performance shares        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Vesting period 3 years      
Percent payout 177.00% 144.00% 93.00%  
Payout percentage in December 2020 for performance period ending September 30, 2020 92.00%      
Maximum potential shares to be delivered in payment under performance share awards (in shares) 32,000      
Weighted average grant date fair value of awards granted (in dollars per share) $ 340.77 $ 481.28 $ 298.10  
Total fair value of shares vested $ 12.5 $ 23.4 $ 7.4  
Shares granted in the period (in shares) 66,000      
Performance shares | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Percent payout 0.00% 0.00% 0.00% 0.00%
Performance shares | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Percent payout 200.00% 200.00% 200.00% 200.00%
Restricted stock and restricted stock units        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Weighted average grant date fair value of awards granted (in dollars per share) $ 263.67 $ 298.44 $ 265.32  
Total fair value of shares vested $ 54.4 $ 35.6 $ 10.4  
Shares granted in the period (in shares) 245,000      
Restricted stock and restricted stock units | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Vesting period 1 year      
Restricted stock and restricted stock units | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Vesting period 5 years      
Unrestricted stock        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Weighted average grant date fair value of awards granted (in dollars per share) $ 261.56 $ 345.00 $ 228.80  
Shares granted in the period (in shares) 6,600      
2020 Long Term Incentive Plan        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Shares authorized (up to) (in shares)     13,000,000  
Shares available for grant (in shares) 8,400,000      
2003 Directors Stock Incentive Plan        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Shares authorized (up to) (in shares)     500,000