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Segment Information - Schedule of Operating Segment (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	May 31, 2024	May 31, 2023	May 31, 2024	May 31, 2023
Segment Reporting Information [Line Items]
Net sales	$ 968.1	$ 1,000.3	$ 2,808.7	$ 2,941.8
Operating profit:	145.3	143.3	396.3	363.7
Operating Segments | ABL
Segment Reporting Information [Line Items]
Net sales	898.5	940.7	2,618.4	2,778.6
Operating profit:	151.5	150.0	421.3	391.7
Operating Segments | ISG
Segment Reporting Information [Line Items]
Net sales	75.7	65.8	208.0	180.8
Operating profit:	12.5	8.6	26.9	22.7
Eliminations
Segment Reporting Information [Line Items]
Net sales	(6.1)	(6.2)	(17.7)	(17.6)
Unallocated corporate amounts
Segment Reporting Information [Line Items]
Operating profit:	$ (18.7)	$ (15.3)	$ (51.9)	$ (50.7)

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