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Segment Reporting - Schedule of Income Before Income Taxes (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Feb. 29, 2024	Feb. 28, 2023	Feb. 29, 2024	Feb. 28, 2023
Segment Reporting Information [Line Items]
Operating profit	$ 118.1	$ 111.5	$ 251.0	$ 220.4
Interest (income) expense, net	(0.1)	5.7	0.8	12.3
Miscellaneous expense (income), net	0.6	(3.7)	1.7	5.4
Income before income taxes	117.6	109.5	248.5	202.7
Operating Segments | ABL
Segment Reporting Information [Line Items]
Operating profit	126.0	123.6	269.8	241.7
Operating Segments | ISG
Segment Reporting Information [Line Items]
Operating profit	9.1	6.3	14.4	14.0
Unallocated corporate amounts
Segment Reporting Information [Line Items]
Operating profit	$ (17.0)	$ (18.4)	$ (33.2)	$ (35.3)

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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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