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Acquisitions - Narrative (Details)
$ in Millions
6 Months Ended 15 Months Ended
Feb. 28, 2021
USD ($)
acquisition
Nov. 30, 2020
USD ($)
Aug. 31, 2020
USD ($)
Feb. 29, 2020
USD ($)
Sep. 17, 2019
brand
Aug. 31, 2019
USD ($)
Business Acquisition [Line Items]            
Number of acquisitions completed | acquisition 0          
Goodwill $ 1,084.2   $ 1,080.0 $ 1,089.6   $ 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