Significant Accounting Policies - Changes of Accumulated Other Comprehensive Loss, Net of Tax (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 31, 2025	Aug. 31, 2024	Aug. 31, 2023
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	$ 2,378.8	$ 2,015.4	$ 1,911.8
Other comprehensive (loss) income before reclassifications	12.9	(4.9)
Amounts reclassified from accumulated other comprehensive loss	25.5	2.6
Other comprehensive income (loss) items, net of tax	38.4	(2.3)	13.2
Ending balance	2,724.9	2,378.8	2,015.4
Accumulated Other Comprehensive Loss Items
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(114.9)	(112.6)	(125.8)
Other comprehensive income (loss) items, net of tax	38.4	(2.3)	13.2
Ending balance	(76.5)	(114.9)	(112.6)
Foreign Currency Items
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(70.9)	(65.0)
Other comprehensive (loss) income before reclassifications	10.8	(5.9)
Amounts reclassified from accumulated other comprehensive loss	0.0	0.0
Other comprehensive income (loss) items, net of tax	10.8	(5.9)
Ending balance	(60.1)	(70.9)	(65.0)
Defined Benefit Pension Plans
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(44.0)	(47.6)
Other comprehensive (loss) income before reclassifications	2.1	1.0
Amounts reclassified from accumulated other comprehensive loss	25.5	2.6
Other comprehensive income (loss) items, net of tax	27.6	3.6
Ending balance	$ (16.4)	$ (44.0)	$ (47.6)

Amount of equity (deficit) attributable to parent. Excludes temporary equity and equity attributable to noncontrolling interest.

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