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Inventories - Schedule of Inventories (Details) - USD ($) $ in Millions	Mar. 01, 2025	Aug. 31, 2024
Inventory Disclosure [Abstract]
Finished goods	$ 100.9	$ 81.3
Work-in-process	142.5	171.9
Raw materials	268.5	237.6
Total	511.9	490.8
Less: Excess of First-in, first-out ("FIFO") over LIFO cost	51.7	52.1
Inventories, net	$ 460.2	$ 438.7

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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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-Topic 210
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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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Amount before valuation and LIFO reserves of raw materials expected to be sold, or consumed within one year or operating cycle, if longer.

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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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