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Supplemental Disaggregated Information (Details) - USD ($)
$ in Millions
12 Months Ended
Aug. 31, 2021
Aug. 31, 2020
Aug. 31, 2019
Geographic Distribution      
Net sales $ 3,461.0 $ 3,326.3 $ 3,672.7
Operating profit: 427.6 353.9 462.9
Income before income taxes: 396.2 324.7 424.9
Long-lived assets 361.0 363.4 295.0
Domestic      
Geographic Distribution      
Net sales 2,982.4 2,925.0 3,277.4
Operating profit: 369.9 300.6 419.3
Income before income taxes: 343.7 274.2 386.4
Long-lived assets 284.4 298.6 246.9
International      
Geographic Distribution      
Net sales 478.6 401.3 395.3
Operating profit: 57.7 53.3 43.6
Income before income taxes: 52.5 50.5 38.5
Long-lived assets $ 76.6 $ 64.8 $ 48.1
Net Sales | Product Concentration Risk | Lighting and Building Management Solutions      
Geographic Distribution      
Sales as percentage of total sales (percent) 99.00% 99.00% 99.00%