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Acquisitions - Narrative (Details)
$ in Millions
3 Months Ended
Nov. 30, 2020
USD ($)
brand
acquisition
Aug. 31, 2020
USD ($)
Nov. 30, 2019
USD ($)
Aug. 31, 2019
USD ($)
Business Acquisition [Line Items]        
Number of acquisitions completed | acquisition 0      
Goodwill $ 1,080.6 $ 1,080.0 $ 1,115.5 $ 967.3
The Luminaires Group (TLG)        
Business Acquisition [Line Items]        
Number of niche lighting brands | brand 5      
Fiscal 2020 Acquisitions        
Business Acquisition [Line Items]        
Goodwill $ 107.6      
Identified intangible assets $ 180.6      
Weighted average useful life of acquired intangible assets 16 years      
Goodwill expected to be tax deductible $ 77.7