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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, 2025
Aug. 31, 2024
Aug. 31, 2023
AOCI Attributable to Parent, Net of Tax [Roll Forward]      
Beginning balance $ 2,378.8 $ 2,015.4 $ 1,911.8
Other comprehensive (loss) income before reclassifications 12.9 (4.9)  
Amounts reclassified from accumulated other comprehensive loss 25.5 2.6  
Other comprehensive income (loss) items, net of tax 38.4 (2.3) 13.2
Ending balance 2,724.9 2,378.8 2,015.4
Accumulated Other Comprehensive Loss Items      
AOCI Attributable to Parent, Net of Tax [Roll Forward]      
Beginning balance (114.9) (112.6) (125.8)
Other comprehensive income (loss) items, net of tax 38.4 (2.3) 13.2
Ending balance (76.5) (114.9) (112.6)
Foreign Currency Items      
AOCI Attributable to Parent, Net of Tax [Roll Forward]      
Beginning balance (70.9) (65.0)  
Other comprehensive (loss) income before reclassifications 10.8 (5.9)  
Amounts reclassified from accumulated other comprehensive loss 0.0 0.0  
Other comprehensive income (loss) items, net of tax 10.8 (5.9)  
Ending balance (60.1) (70.9) (65.0)
Defined Benefit Pension Plans      
AOCI Attributable to Parent, Net of Tax [Roll Forward]      
Beginning balance (44.0) (47.6)  
Other comprehensive (loss) income before reclassifications 2.1 1.0  
Amounts reclassified from accumulated other comprehensive loss 25.5 2.6  
Other comprehensive income (loss) items, net of tax 27.6 3.6  
Ending balance $ (16.4) $ (44.0) $ (47.6)