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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, 2024
Aug. 31, 2023
Aug. 31, 2022
AOCI Attributable to Parent, Net of Tax [Roll Forward]      
Beginning balance $ 2,015.4 $ 1,911.8 $ 2,044.5
Other comprehensive income before reclassifications (4.9) 8.9  
Amounts reclassified from accumulated other comprehensive loss 2.6 4.3  
Other comprehensive (loss) income items, net of tax (2.3) 13.2 (27.6)
Ending balance 2,378.8 2,015.4 1,911.8
Accumulated Other Comprehensive Loss Items      
AOCI Attributable to Parent, Net of Tax [Roll Forward]      
Beginning balance (112.6) (125.8) (98.2)
Other comprehensive (loss) income items, net of tax (2.3) 13.2 (27.6)
Ending balance (114.9) (112.6) (125.8)
Foreign Currency Items      
AOCI Attributable to Parent, Net of Tax [Roll Forward]      
Beginning balance (65.0) (73.5)  
Other comprehensive income before reclassifications (5.9) 8.5  
Amounts reclassified from accumulated other comprehensive loss 0.0 0.0  
Other comprehensive (loss) income items, net of tax (5.9) 8.5  
Ending balance (70.9) (65.0) (73.5)
Defined Benefit Pension Plans      
AOCI Attributable to Parent, Net of Tax [Roll Forward]      
Beginning balance (47.6) (52.3)  
Other comprehensive income before reclassifications 1.0 0.4  
Amounts reclassified from accumulated other comprehensive loss 2.6 4.3  
Other comprehensive (loss) income items, net of tax 3.6 4.7  
Ending balance $ (44.0) $ (47.6) $ (52.3)