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Property, Plant, and Equipment - Schedule of Property, Plant, and Equipment (Details) - USD ($)
$ in Millions
May 31, 2023
Aug. 31, 2022
Property, Plant and Equipment [Line Items]    
Total property, plant, and equipment, at cost $ 940.5 $ 891.9
Less: Accumulated depreciation and amortization (650.1) (615.4)
Property, plant, and equipment, net 290.4 276.5
Land    
Property, Plant and Equipment [Line Items]    
Total property, plant, and equipment, at cost 22.7 22.0
Buildings and leasehold improvements    
Property, Plant and Equipment [Line Items]    
Total property, plant, and equipment, at cost 207.6 202.3
Machinery and equipment    
Property, Plant and Equipment [Line Items]    
Total property, plant, and equipment, at cost $ 710.2 $ 667.6