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Segment Information (Details) $ in Millions	3 Months Ended
	Nov. 30, 2022 USD ($) segment	Nov. 30, 2021 USD ($)
Segment Reporting [Abstract]
Number of reportable segments | segment	2
Special charges	$ 6.9	$ 0.0
Segment Reporting Information [Line Items]
Net sales	997.9	926.1
Operating profit (loss)	108.9	115.1
Depreciation and amortization	26.5	24.3
Interest expense, net	6.6	5.9
Miscellaneous expense, net	9.1	0.3
Income before income taxes	93.2	108.9
ABL
Segment Reporting [Abstract]
Special charges	6.9
Operating segments | ABL
Segment Reporting Information [Line Items]
Net sales	947.1	883.6
Operating profit (loss)	118.1	128.1
Depreciation and amortization	22.7	20.4
Operating segments | ISG
Segment Reporting Information [Line Items]
Net sales	56.8	46.4
Operating profit (loss)	7.7	2.0
Depreciation and amortization	3.5	3.6
Corporate
Segment Reporting Information [Line Items]
Net sales	0.0	0.0
Operating profit (loss)	(16.9)	(15.0)
Depreciation and amortization	0.3	0.3
Eliminations
Segment Reporting Information [Line Items]
Net sales	(6.0)	(3.9)
Operating profit (loss)	0.0	0.0
Depreciation and amortization	$ 0.0	$ 0.0

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