Inventories - Schedule of Inventories (Details) - USD ($) $ in Millions	Aug. 26, 2023	Aug. 27, 2022
Inventory Disclosure [Abstract]
Finished goods	$ 53.0	$ 59.3
Work-in-process ("WIP")	159.9	198.9
Raw materials	305.6	315.0
Total	518.5	573.2
Less: Excess of FIFO over LIFO cost	47.9	47.4
Inventories, net	$ 470.6	$ 525.8

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Amount before valuation and LIFO reserves of completed merchandise or goods expected to be sold within one year or operating cycle, if longer.

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Gross amount, as of the balance sheet date, of merchandise, goods, commodities, or supplies held for future sale or to be used in manufacturing, servicing or production process.

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Amount by which inventory stated at last-in first-out (LIFO) is less than (in excess of) inventory stated at other inventory cost methods.

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Amount after valuation and LIFO reserves of inventory expected to be sold, or consumed within one year or operating cycle, if longer.

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Carrying amount, net of valuation reserves and adjustments, as of the balance sheet date of unprocessed items to be consumed in the manufacturing or production process.

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Amount before valuation and LIFO reserves of merchandise or goods in the production process expected to be completed within one year or operating cycle, if longer.

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