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Product Warranties (Details) - USD ($)
$ in Millions
3 Months Ended
Nov. 26, 2022
Nov. 27, 2021
Movement in Standard and Extended Product Warranty, Increase (Decrease) [Roll Forward]    
Balance at beginning of period $ 127.9 $ 91.2
Business acquisition 0.0 4.7
Provision 18.1 26.1
Claims paid (23.8) (19.6)
Balance at end of period $ 122.2 $ 102.4