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Inventories - Schedule of Inventories (Details) - USD ($)
$ in Millions
May 25, 2024
Aug. 26, 2023
Inventory Disclosure [Abstract]    
Finished goods $ 67.4 $ 53.0
Work-in-process 155.7 159.9
Raw materials 266.2 305.6
Total 489.3 518.5
Less: Excess of First-in, first-out ("FIFO") over LIFO cost 47.8 47.9
Inventories, net $ 441.5 $ 470.6