New Accounting Pronouncements (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Feb. 24, 2019	Feb. 25, 2018	Feb. 24, 2019	Feb. 25, 2018	Aug. 26, 2018
Increase (decrease) to benefit plan non-service income, impact of adoption of new accounting standard	$ (21.4)	$ (23.2)	$ (63.3)	$ (64.5)
Cumulative effect adjustment related to adoption of new accounting standard					$ (33.9)
Retained Earnings [Member]
Cumulative effect adjustment related to adoption of new accounting standard					$ (33.9)
Accounting Standards Update 2017-07 [Member]
Increase (decrease) to benefit plan non-service income, impact of adoption of new accounting standard	(21.4)	(23.2)	(63.3)	(64.5)
Increase (decrease) to operating profit, impact of adoption of new accounting standard	(21.4)	$ (23.2)	(63.3)	$ (64.5)
Accounting Standards Update 2014-09 [Member] | Deferred Income Tax Charges [Member]
Cumulative effect adjustment related to adoption of new accounting standard	(11.4)		(11.4)
Accounting Standards Update 2014-09 [Member] | Other Current Liabilities [Member]
Cumulative effect adjustment related to adoption of new accounting standard	45.3		45.3
Accounting Standards Update 2014-09 [Member] | Retained Earnings [Member]
Cumulative effect adjustment related to adoption of new accounting standard	$ (33.9)		$ (33.9)