Goodwill and Intangible Assets - Schedule of Intangible Assets (Details) - USD ($) $ in Millions	May 27, 2023	Aug. 27, 2022
Schedule of Intangible Assets [Line Items]
Gross Carrying Amount	$ 628.5	$ 581.2
Accumulated Amortization	120.8	108.8
Net Carrying Value	507.7	472.4
Dealer networks/customer relationships
Schedule of Intangible Assets [Line Items]
Gross Carrying Amount	183.6	180.0
Accumulated Amortization	71.6	60.5
Net Carrying Value	112.0	119.5
Backlog
Schedule of Intangible Assets [Line Items]
Gross Carrying Amount	43.6	42.3
Accumulated Amortization	42.4	42.3
Net Carrying Value	1.2	0.0
Developed technology
Schedule of Intangible Assets [Line Items]
Gross Carrying Amount	38.3
Accumulated Amortization	0.5
Net Carrying Value	37.8
Non-compete agreements
Schedule of Intangible Assets [Line Items]
Gross Carrying Amount	6.6	6.6
Accumulated Amortization	6.3	6.0
Net Carrying Value	0.3	0.6
Trade names
Schedule of Intangible Assets [Line Items]
Gross Carrying Amount	356.4	352.3
Net Carrying Value	$ 356.4	$ 352.3