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Share-Based Compensation - Narrative (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Pre-tax share-based compensation expense $ 68.1 $ 51.7 $ 46.1  
Income tax benefit related to share-based compensation expense 11.2 $ 8.6 $ 7.7  
Unrecognized compensation cost related to share-based compensation awards, net of estimated forfeitures $ 101.9      
Weighted average period for recognition of total unrecognized compensation cost 2 years      
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) $ 87.68 $ 55.50 $ 35.80  
Total intrinsic value of stock options exercised $ 52.8 $ 108.4 $ 151.6  
Performance shares        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Vesting period 3 years      
Percent payout 144.00% 93.00% 77.00%  
Payout percentage in December 2020 for performance period ending September 30, 2020 177.00%      
Maximum potential shares to be delivered in payment under performance share awards (in shares) 48,000      
Weighted average grant date fair value of awards granted (in dollars per share) $ 481.28 $ 298.10 $ 265.04  
Total fair value of shares vested $ 23.4 $ 7.4 $ 5.6  
Shares granted in the period (in shares) 37,000      
Performance shares | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Percent payout 0.00%   0.00% 0.00%
Performance shares | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]        
Percent payout 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) $ 298.44 $ 265.32 $ 200.36  
Total fair value of shares vested $ 35.6 $ 10.4 $ 8.7  
Shares granted in the period (in shares) 252,000      
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) $ 345.00 $ 228.80 $ 171.51  
Shares granted in the period (in shares) 3,300      
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) 10,100,000      
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