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Significant Accounting Policies - Selling, Distribution and Administrative Expenses (Details) - USD ($) $ in Millions | 12 Months Ended
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Aug. 31, 2024 | Aug. 31, 2023 | Aug. 31, 2022
Accounting Policies [Abstract] |  |  |
Other shipping and handling costs | $ 134.2 | $ 141.7 | $ 151.2
Share-based payment expense | 46.6 | 42.0 | 37.4
Income tax benefit for share-based compensation | 8.3 | 7.2 | 9.6
Net excess tax benefit related to share-based payment cost | 1.5 | 1.5 | 4.8
Research and development expense | 102.3 | 97.1 | 95.1
Advertising costs | $ 20.1 | $ 21.9 | $ 19.3

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