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Income Taxes - Schedule of Provision for Income Taxes (Details) - USD ($)
$ in Millions
12 Months Ended
Aug. 31, 2021
Aug. 31, 2020
Aug. 31, 2019
Income Tax Disclosure [Abstract]      
Provision for current federal taxes $ 65.4 $ 54.6 $ 60.3
Provision for current state taxes 12.8 12.5 14.7
Provision for current foreign taxes 14.4 16.0 10.2
(Benefit) provision for deferred taxes (2.7) (6.7) 9.3
Total provision for income taxes $ 89.9 $ 76.4 $ 94.5