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Significant Accounting Policies - Inventories (Details) - USD ($)
$ in Millions
12 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Inventory, Net [Abstract]      
Raw materials, supplies, and work in process $ 214.0 $ 252.6  
Finished goods 180.3 264.0  
Inventories excluding reserves 394.3 516.6  
Less: Reserves (25.8) (30.9)  
Total inventories 368.5 485.7  
Inventory reserves:      
SEC Schedule, 12-09, Valuation and Qualifying Accounts Disclosure [Line Items]      
Balance at Beginning of Year 30.9 38.0 $ 49.3
Additions to reserve 16.2 15.7 21.4
Disposals of reserved inventory (20.6) (22.5) (32.7)
Foreign currency translation adjustments (0.7) (0.3) 0.0
Balance at End of Year $ 25.8 $ 30.9 $ 38.0