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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		6 Months Ended
	Feb. 28, 2025	Feb. 29, 2024	Feb. 28, 2025	Feb. 29, 2024
Accumulated Other Comprehensive Income (Loss) [Line Items]
Other comprehensive (loss) income, before tax	$ (11.1)	$ 1.5	$ (27.7)	$ 0.2
Other comprehensive (loss) income, tax (expense) benefit	(0.1)	(0.1)	(0.3)	(0.3)
Other comprehensive (loss) income items, net of tax	(11.2)	1.4	(28.0)	(0.1)
Foreign currency translation adjustments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Other comprehensive (loss) income, before tax	(11.7)	0.7	(29.0)	(1.4)
Other comprehensive (loss) income, tax (expense) benefit	0.0	0.0	0.0	0.0
Other comprehensive (loss) income items, net of tax	(11.7)	0.7	(29.0)	(1.4)
Actuarial losses on defined benefit pension plans
Accumulated Other Comprehensive Income (Loss) [Line Items]
Other comprehensive (loss) income, before tax	0.6	0.8	1.3	1.6
Other comprehensive (loss) income, tax (expense) benefit	(0.1)	(0.1)	(0.3)	(0.3)
Other comprehensive (loss) income items, net of tax	$ 0.5	$ 0.7	$ 1.0	$ 1.3

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