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Segment Reporting - Income Before Income Taxes (Details) - USD ($) $ in Millions	3 Months Ended
	Nov. 30, 2023	Nov. 30, 2022
Segment Reporting Information [Line Items]
Operating profit	$ 132.9	$ 108.9
Interest expense, net	0.9	6.6
Miscellaneous expense, net	1.1	9.1
Income before income taxes	130.9	93.2
Operating Segments | ABL
Segment Reporting Information [Line Items]
Operating profit	143.8	118.1
Operating Segments | ISG
Segment Reporting Information [Line Items]
Operating profit	5.3	7.7
Unallocated corporate amounts
Segment Reporting Information [Line Items]
Operating profit	$ (16.2)	$ (16.9)

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