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Significant Accounting Policies - Changes of Accumulated Other Comprehensive Loss, Net of Tax (Details) - USD ($)
$ in Millions
 12 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Accumulated Other Comprehensive Loss, Net of Tax [Roll Forward]      
Beginning balance $ 1,911.8 $ 2,044.5 $ 2,127.5
Other comprehensive (loss) income before reclassifications 8.9 (32.6)  
Amounts reclassified from accumulated other comprehensive loss 4.3 5.0  
Other comprehensive income (loss) items, net of tax 13.2 (27.6) 34.5
Ending balance 2,015.4 1,911.8 2,044.5
Accumulated Other Comprehensive Loss Items      
Accumulated Other Comprehensive Loss, Net of Tax [Roll Forward]      
Beginning balance (125.8) (98.2) (132.7)
Other comprehensive income (loss) items, net of tax 13.2 (27.6) 34.5
Ending balance (112.6) (125.8) (98.2)
Foreign Currency Items      
Accumulated Other Comprehensive Loss, Net of Tax [Roll Forward]      
Beginning balance (73.5) (40.2)  
Other comprehensive (loss) income before reclassifications 8.5 (33.3)  
Amounts reclassified from accumulated other comprehensive loss 0.0 0.0  
Other comprehensive income (loss) items, net of tax 8.5 (33.3)  
Ending balance (65.0) (73.5) (40.2)
Defined Benefit Pension Plans      
Accumulated Other Comprehensive Loss, Net of Tax [Roll Forward]      
Beginning balance (52.3) (58.0)  
Other comprehensive (loss) income before reclassifications 0.4 0.7  
Amounts reclassified from accumulated other comprehensive loss 4.3 5.0  
Other comprehensive income (loss) items, net of tax 4.7 5.7  
Ending balance $ (47.6) $ (52.3) $ (58.0)