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Segment Reporting - Income Before Income Taxes (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 31, 2022	Aug. 31, 2021	Aug. 31, 2020
Geographic Distribution
Operating profit (loss)	$ 509.7	$ 427.6	$ 353.9
Interest expense, net	24.9	23.2	23.3
Miscellaneous (income) expense, net	(9.1)	8.2	5.9
Income before income taxes	493.9	396.2	324.7
Operating Segments | ABL
Geographic Distribution
Operating profit (loss)	545.6	476.2	425.8
Operating Segments | ISG
Geographic Distribution
Operating profit (loss)	22.7	9.9	(3.9)
Corporate
Geographic Distribution
Operating profit (loss)	$ (58.6)	$ (58.5)	$ (68.0)

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