Significant Accounting Policies - Inventories (Details) - USD ($) $ in Millions	12 Months Ended
Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2022
Inventory, Net [Abstract]
Raw materials, supplies, and work in process	$ 222.1	$ 214.0
Finished goods	191.1	180.3
Inventories excluding reserves	413.2	394.3
Less: Reserves	(25.6)	(25.8)
Total inventories	387.6	368.5
Inventory reserves:
SEC Schedule, 12-09, Valuation and Qualifying Accounts Disclosure [Line Items]
Balance at Beginning of Year	25.8	30.9	$ 38.0
Additions to reserve	10.9	16.2	15.7
Disposals of reserved inventory	(11.0)	(20.6)	(22.5)
Foreign currency translation adjustments	(0.1)	(0.7)	(0.3)
Balance at End of Year	$ 25.6	$ 25.8	$ 30.9

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