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Acquisitions and Divestitures (Details) $ in Millions	3 Months Ended	6 Months Ended
	Nov. 30, 2022 USD ($)	Feb. 29, 2024 USD ($) divestiture	Aug. 31, 2023 USD ($)	Feb. 28, 2023 USD ($)	Oct. 30, 2022 USD ($)	Aug. 31, 2022 USD ($)
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Goodwill		$ 1,097.1	$ 1,097.9	$ 1,080.3		$ 1,084.3
Number of divestitures | divestiture		0
ISG
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Goodwill		$ 83.3	$ 83.5	$ 68.0		$ 70.1
KE2 Therm Solutions, Inc
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Goodwill		15.0
Identified intangible assets		$ 18.0
Weighted average amortization period (in years)		15 years
Measurement period adjustments		$ 0.0
Sunoptics Prismatic Skylights Business | Disposal Group, Not Discontinued Operations
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Assets transferred					$ 15.1
Pre-tax loss on the sale	$ 11.2

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