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Property, Plant, and Equipment - Schedule of Property, Plant, and Equipment (Details) - USD ($)
$ in Millions
Feb. 29, 2024
Aug. 31, 2023
Property, Plant and Equipment [Line Items]    
Total property, plant, and equipment, at cost $ 981.2 $ 961.8
Less: Accumulated depreciation and amortization (685.2) (664.2)
Property, plant, and equipment, net 296.0 297.6
Land    
Property, Plant and Equipment [Line Items]    
Total property, plant, and equipment, at cost 23.0 23.0
Buildings and leasehold improvements    
Property, Plant and Equipment [Line Items]    
Total property, plant, and equipment, at cost 214.7 210.9
Machinery and equipment    
Property, Plant and Equipment [Line Items]    
Total property, plant, and equipment, at cost $ 743.5 $ 727.9