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Commitments and Contingencies - Product Warranty and Recall Costs (Details) - USD ($)
$ in Millions
12 Months Ended
Aug. 31, 2022
Aug. 31, 2021
Aug. 31, 2020
Movement in warranty accruals      
Beginning balance $ 20.3 $ 16.1 $ 11.5
Warranty and recall costs 52.4 32.3 32.0
Payments and other deductions (45.4) (28.4) (27.5)
Acquired warranty and recall liabilities 0.0 0.3 0.1
Ending balance $ 27.3 $ 20.3 $ 16.1