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Significant Accounting Policies - Property, Plant and Equipment (Details) - USD ($)
$ in Millions
 12 Months Ended
Aug. 31, 2025
Aug. 31, 2024
Aug. 31, 2023
Property, Plant and Equipment [Line Items]      
Depreciation expense $ 56.6 $ 51.4 $ 51.1
Total property, plant, and equipment, at cost 1,096.9 999.7  
Less: Accumulated depreciation and amortization (753.7) (695.8)  
Property, plant, and equipment, net 343.2 303.9  
Land      
Property, Plant and Equipment [Line Items]      
Total property, plant, and equipment, at cost 22.2 22.3  
Buildings and leasehold improvements      
Property, Plant and Equipment [Line Items]      
Total property, plant, and equipment, at cost 235.3 218.7  
Machinery, equipment, and information technology      
Property, Plant and Equipment [Line Items]      
Total property, plant, and equipment, at cost $ 839.4 $ 758.7  
Minimum | Buildings and leasehold improvements      
Property, Plant and Equipment [Line Items]      
Useful lives of plant and equipment, minimum 3 years    
Minimum | Machinery, equipment, and information technology      
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, equipment, and information technology      
Property, Plant and Equipment [Line Items]      
Useful lives of plant and equipment, minimum 15 years