Income Taxes - Income (Loss) Before Income Taxes (Details) - USD ($) $ in Millions	12 Months Ended
Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2022
Income Tax Disclosure [Abstract]
Domestic	$ 472.4	$ 367.5	$ 409.6
International	76.2	79.2	84.3
Income before income taxes	$ 548.6	$ 446.7	$ 493.9

Amount of income (loss) from continuing operations, including income (loss) from equity method investments, before deduction of income tax expense (benefit), and income (loss) attributable to noncontrolling interest.

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+ Details