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Share-based Payments - Share-based Compensation Expense Recognized (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2022
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based payment expense	$ 46.6	$ 42.0	$ 37.4
Stock Incentive Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based payment expense	46.6	42.0	37.4
Restricted stock awards and units | Stock Incentive Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based payment expense	23.9	19.6	17.2
Performance stock units | Stock Incentive Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based payment expense	18.6	15.2	9.9
Stock options | Stock Incentive Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based payment expense	2.6	5.7	8.8
Director stock units | Stock Incentive Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based payment expense	$ 1.5	$ 1.5	$ 1.5

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- Definition

Amount of expense for award under share-based payment arrangement. Excludes amount capitalized.

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