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Comprehensive Income - Schedule of Tax Expense or Benefit Allocated to Each Component of Other Comprehensive Loss (Details) - USD ($)
$ in Millions
 3 Months Ended
Nov. 30, 2024
Nov. 30, 2023
Accumulated Other Comprehensive Income (Loss) [Line Items]    
Other comprehensive (loss) income, before tax $ (16.6) $ (1.3)
Other comprehensive (loss) income, tax (expense) benefit (0.2) (0.2)
Other comprehensive loss items, net of tax (16.8) (1.5)
Foreign currency translation adjustments    
Accumulated Other Comprehensive Income (Loss) [Line Items]    
Other comprehensive (loss) income, before tax (17.3) (2.1)
Other comprehensive (loss) income, tax (expense) benefit 0.0 0.0
Other comprehensive loss items, net of tax (17.3) (2.1)
Actuarial losses on defined benefit pension plans    
Accumulated Other Comprehensive Income (Loss) [Line Items]    
Other comprehensive (loss) income, before tax 0.7 0.8
Other comprehensive (loss) income, tax (expense) benefit (0.2) (0.2)
Other comprehensive loss items, net of tax $ 0.5 $ 0.6