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Property, Plant, and Equipment - Schedule of Property, Plant, and Equipment (Details) - USD ($)
$ in Millions
Nov. 30, 2022
Aug. 31, 2022
Property, Plant and Equipment [Line Items]    
Total property, plant, and equipment, at cost $ 906.1 $ 891.9
Less: Accumulated depreciation and amortization (626.5) (615.4)
Property, plant, and equipment, net 279.6 276.5
Land    
Property, Plant and Equipment [Line Items]    
Total property, plant, and equipment, at cost 22.2 22.0
Buildings and leasehold improvements    
Property, Plant and Equipment [Line Items]    
Total property, plant, and equipment, at cost 202.8 202.3
Machinery and equipment    
Property, Plant and Equipment [Line Items]    
Total property, plant, and equipment, at cost $ 681.1 $ 667.6