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Acquisitions (Details)
$ in Millions
12 Months Ended
Aug. 31, 2022
USD ($)
acquisition
Aug. 31, 2021
USD ($)
Aug. 31, 2020
USD ($)
Sep. 17, 2019
brand
Business Acquisition [Line Items]        
Number of acquisitions | acquisition 0      
Cash outflows for working capital settlements $ (12.9)      
Goodwill 1,084.3 $ 1,094.7 $ 1,080.0  
Fiscal 2021 Acquisitions        
Business Acquisition [Line Items]        
Goodwill 12.3      
Identifiable intangible assets $ 6.7      
Weighted average amortization period in years 11 years      
Goodwill expected to be tax deductible $ 9.2      
The Luminaires Group (TLG)        
Business Acquisition [Line Items]        
Number of niche lighting brands of acquired entity | brand       5
Fiscal 2020 Acquisitions        
Business Acquisition [Line Items]        
Goodwill 107.6      
Identifiable intangible assets $ 180.6      
Weighted average amortization period in years 16 years      
Goodwill expected to be tax deductible $ 77.7