Significant Accounting Policies - Selling, Distribution and Administrative Expenses (Details) - USD ($) $ in Millions	12 Months Ended
	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