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Segment Information - Operating Segment (Details) $ in Millions	12 Months Ended
	Aug. 31, 2022 USD ($) segment	Aug. 31, 2021 USD ($)	Aug. 31, 2020 USD ($)
Segment Reporting [Abstract]
Number of reportable segments | segment	2
Segment Reporting Information [Line Items]
Net sales	$ 4,006.1	$ 3,461.0	$ 3,326.3
Operating profit (loss)	509.7	427.6	353.9
Depreciation and amortization	94.8	100.1	101.1
Operating Segments | ABL
Segment Reporting Information [Line Items]
Net sales	3,810.1	3,287.3	3,180.9
Operating profit (loss)	545.6	476.2	425.8
Depreciation and amortization	79.3	84.3	83.7
Operating Segments | ISG
Segment Reporting Information [Line Items]
Net sales	216.1	190.0	157.0
Operating profit (loss)	22.7	9.9	(3.9)
Depreciation and amortization	14.4	14.7	16.3
Corporate
Segment Reporting Information [Line Items]
Net sales	0.0	0.0	0.0
Operating profit (loss)	(58.6)	(58.5)	(68.0)
Depreciation and amortization	1.1	1.1	1.1
Eliminations
Segment Reporting Information [Line Items]
Net sales	(20.1)	(16.3)	(11.6)
Operating profit (loss)	0.0	0.0	0.0
Depreciation and amortization	$ 0.0	$ 0.0	$ 0.0

X

- Definition

The aggregate expense recognized in the current period that allocates the cost of tangible assets, intangible assets, or depleting assets to periods that benefit from use of the assets.

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