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Significant Accounting Policies - Property, Plant and Equipment (Details) - USD ($)
$ in Millions
 12 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Property, Plant and Equipment [Line Items]      
Depreciation expense $ 51.1 $ 53.8 $ 59.4
Total property, plant, and equipment, at cost 961.8 891.9  
Less: Accumulated depreciation and amortization (664.2) (615.4)  
Property, plant, and equipment, net 297.6 276.5  
Land      
Property, Plant and Equipment [Line Items]      
Total property, plant, and equipment, at cost 23.0 22.0  
Buildings and leasehold improvements      
Property, Plant and Equipment [Line Items]      
Total property, plant, and equipment, at cost 210.9 202.3  
Machinery and equipment      
Property, Plant and Equipment [Line Items]      
Total property, plant, and equipment, at cost $ 727.9 $ 667.6  
Minimum | Buildings and leasehold improvements      
Property, Plant and Equipment [Line Items]      
Useful lives of plant and equipment, minimum 3 years    
Minimum | Machinery and equipment      
Property, Plant and Equipment [Line Items]      
Useful lives of plant and equipment, minimum 2 years    
Maximum | Buildings and leasehold improvements      
Property, Plant and Equipment [Line Items]      
Useful lives of plant and equipment, minimum 40 years    
Maximum | Machinery and equipment      
Property, Plant and Equipment [Line Items]      
Useful lives of plant and equipment, minimum 15 years