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Inventories - Schedule of Inventories (Details) - USD ($) $ in Millions | Aug. 26, 2023 | Aug. 27, 2022
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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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