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Segment Information (Details) $ in Millions	3 Months Ended			6 Months Ended
	Feb. 28, 2023 USD ($)	Nov. 30, 2022 USD ($)	Feb. 28, 2022 USD ($)	Feb. 28, 2023 USD ($) segment	Feb. 28, 2022 USD ($)
Segment Reporting Information [Line Items]
Number of reportable segments | segment				2
Special charges	$ 0.0	$ 6.9	$ 0.0	$ 6.9	$ 0.0
Net sales	943.6		909.1	1,941.5	1,835.2
Operating profit (loss)	111.5		102.3	220.4	217.4
Depreciation and amortization	22.0		23.6	48.5	47.9
Interest expense, net	5.7		6.0	12.3	11.9
Miscellaneous (income) expense, net	(3.7)		(1.9)	5.4	(1.6)
Income before income taxes	109.5		98.2	202.7	207.1
ABL
Segment Reporting Information [Line Items]
Special charges				6.9
Operating Segments | ABL
Segment Reporting Information [Line Items]
Net sales	890.8		863.1	1,837.9	1,746.7
Operating profit (loss)	123.6		116.5	241.7	244.6
Depreciation and amortization	18.2		19.8	40.9	40.2
Operating Segments | ISG
Segment Reporting Information [Line Items]
Net sales	58.2		50.0	115.0	96.4
Operating profit (loss)	6.3		1.2	14.0	3.2
Depreciation and amortization	3.5		3.6	7.0	7.2
Corporate
Segment Reporting Information [Line Items]
Net sales	0.0		0.0	0.0	0.0
Operating profit (loss)	(18.4)		(15.4)	(35.3)	(30.4)
Depreciation and amortization	0.3		0.2	0.6	0.5
Eliminations
Segment Reporting Information [Line Items]
Net sales	(5.4)		(4.0)	(11.4)	(7.9)
Operating profit (loss)	0.0		0.0	0.0	0.0
Depreciation and amortization	$ 0.0		$ 0.0	$ 0.0	$ 0.0

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