Significant Accounting Policies - Goodwill and Other Intangibles (Details)	12 Months Ended
	Aug. 31, 2023 USD ($) intangible_asset	Aug. 31, 2022 USD ($)	Aug. 31, 2021 USD ($)	Jun. 01, 2023 USD ($) intangible_asset
Goodwill [Roll Forward]
Beginning balance	$ 1,084,300,000	$ 1,094,700,000
Additions from acquired businesses	15,200,000
Adjustments to provisional amounts from acquired businesses	(200,000)	2,300,000
Derecognitions for divestitures	(700,000)
Foreign currency translation adjustments	(700,000)	(12,700,000)
Ending balance	1,097,900,000	1,084,300,000	$ 1,094,700,000
Gross Carrying Amount	691,100,000	677,500,000
Accumulated Amortization	(345,500,000)	(322,000,000.0)
Indefinite-lived trade names				$ 173,400,000
Amortization expense of finite-lived intangible assets	42,100,000	41,000,000	40,700,000
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]
Amortization expense in fiscal 2024	39,600,000
Amortization expense in fiscal 2025	32,200,000
Amortization expense in fiscal 2026	29,500,000
Amortization expense in fiscal 2027	28,000,000
Amortization expense in fiscal 2028	23,900,000
Goodwill impairment charge	0	0	0
Indefinite-lived intangible assets held | intangible_asset				13
Indefinite-lived intangible assets				$ 173,400,000
Trade Names
Goodwill [Roll Forward]
Indefinite-lived trade names	135,600,000	173,700,000
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]
Indefinite-lived intangible assets	135,600,000	173,700,000
Intangible asset impairment charge	$ 14,000,000
Number of impaired intangible assets | intangible_asset	6
Number of unimpaired intangible assets | intangible_asset	7
Patents and patented technology
Goodwill [Roll Forward]
Gross Carrying Amount	$ 158,800,000	160,800,000
Accumulated Amortization	(122,300,000)	(116,000,000.0)
Trademarks and trade names
Goodwill [Roll Forward]
Gross Carrying Amount	45,500,000	27,200,000
Accumulated Amortization	(18,400,000)	(18,300,000)
Distribution network
Goodwill [Roll Forward]
Gross Carrying Amount	61,800,000	61,800,000
Accumulated Amortization	(49,400,000)	(47,300,000)
Customer relationships
Goodwill [Roll Forward]
Gross Carrying Amount	425,000,000.0	427,700,000
Accumulated Amortization	(155,400,000)	(140,400,000)
ABL
Goodwill [Roll Forward]
Beginning balance	1,014,200,000	1,022,200,000
Additions from acquired businesses	0
Adjustments to provisional amounts from acquired businesses	0	2,300,000
Derecognitions for divestitures	(700,000)
Foreign currency translation adjustments	900,000	(10,300,000)
Ending balance	1,014,400,000	1,014,200,000	1,022,200,000
ISG
Goodwill [Roll Forward]
Beginning balance	70,100,000	72,500,000
Additions from acquired businesses	15,200,000
Adjustments to provisional amounts from acquired businesses	(200,000)	0
Derecognitions for divestitures	0
Foreign currency translation adjustments	(1,600,000)	(2,400,000)
Ending balance	$ 83,500,000	$ 70,100,000	$ 72,500,000