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Inventories - Schedule of Inventories (Details) - USD ($) $ in Millions | Nov. 25, 2023 | Aug. 26, 2023
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Inventory Disclosure [Abstract] |  |
Finished goods | $ 64.0 | $ 53.0
Work-in-process | 145.7 | 159.9
Raw materials | 332.3 | 305.6
Total | 542.0 | 518.5
Less: Excess of First-in, first-out ("FIFO") over LIFO cost | 48.0 | 47.9
Inventories, net | $ 494.0 | $ 470.6

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