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Goodwill and Intangible Assets - Changes in Goodwill (Details) - USD ($) $ in Millions	3 Months Ended
	Nov. 30, 2023	Nov. 30, 2022
Goodwill [Roll Forward]
Goodwill, beginning balance	$ 1,097.9	$ 1,084.3
Derecognitions for divestitures		(0.7)
Foreign currency translation adjustments	(0.4)	(1.6)
Goodwill, ending balance	1,097.5	1,082.0
ABL
Goodwill [Roll Forward]
Goodwill, beginning balance	1,014.4	1,014.2
Derecognitions for divestitures		(0.7)
Foreign currency translation adjustments	(0.2)	(0.4)
Goodwill, ending balance	1,014.2	1,013.1
ISG
Goodwill [Roll Forward]
Goodwill, beginning balance	83.5	70.1
Derecognitions for divestitures		0.0
Foreign currency translation adjustments	(0.2)	(1.2)
Goodwill, ending balance	$ 83.3	$ 68.9

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- Definition

Amount after accumulated impairment loss of an asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized.

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