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Acquisitions (Details)
$ in Millions
12 Months Ended
Aug. 31, 2021
USD ($)
Aug. 31, 2020
USD ($)
Sep. 17, 2019
brand
Aug. 31, 2019
USD ($)
Business Acquisition [Line Items]        
Goodwill $ 1,094.7 $ 1,080.0   $ 967.3
Weighted Average Amortization Period in Years 19 years      
Fiscal 2021 Acquisitions        
Business Acquisition [Line Items]        
Goodwill $ 10.0      
Identifiable intangible assets $ 6.1      
Weighted Average Amortization Period in Years 11 years      
Goodwill expected to be tax deductible $ 6.9      
The Luminaires Group (TLG)        
Business Acquisition [Line Items]        
Number of niche lighting brands of acquired entity | brand     5  
Fiscal 2020 and Fiscal 2019 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