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Business Combinations (Details) - USD ($) shares in Millions, $ in Millions		3 Months Ended			9 Months Ended
	Aug. 31, 2021	May 27, 2023	May 28, 2022	Nov. 27, 2021	May 27, 2023	May 28, 2022	Apr. 28, 2023	Aug. 27, 2022	Aug. 28, 2021
Business Acquisition [Line Items]
Acquisition-related costs expensed		$ 3.9	$ 0.7		$ 5.6	$ 4.6
Issuance of stock for acquisition						22.0
Goodwill		514.5	484.2		514.5	$ 484.2		$ 484.2	$ 348.1
Lithionics
Business Acquisition [Line Items]
Percent of voting interest acquired							100.00%
Acquisition-related costs expensed		3.1
Barletta
Business Acquisition [Line Items]
Percent of voting interest acquired	100.00%
Acquisition-related costs expensed				$ 2.4
Purchase price	$ 286.3
Cash payments	240.1
Purchase price, common stock issued	$ 25.0
Discount percentage on purchase price	12.00%
Lockup restriction period	1 year
Purchase price, common stock issued after discount	$ 22.0
Earnout liability	24.2	19.8			19.8			39.8
Issuance of stock for acquisition			$ 22.0
Issuance of stock for acquisition (in shares)			0.2
Goodwill	136.1
Other intangible assets	$ 111.4
Transaction costs				$ 3.1
Barletta | Backlog
Business Acquisition [Line Items]
Weighted-average useful life	10 months
Barletta | Dealer networks/customer relationships
Business Acquisition [Line Items]
Weighted-average useful life	12 years
Barletta | Other Current Liabilities
Business Acquisition [Line Items]
Earnout liability		$ 19.8			$ 19.8			21.3
Barletta | Other Noncurrent Liabilities
Business Acquisition [Line Items]
Earnout liability								$ 18.5
Barletta | Earnout Paid In Stock
Business Acquisition [Line Items]
Earnout amount	$ 50.0
Barletta | Earnout Paid In Cash
Business Acquisition [Line Items]
Earnout amount	$ 15.0

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Weighted average amortization period of finite-lived intangible assets acquired either individually or as part of a group of assets, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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