Business Segment and Geographic Information (Schedule of net sales by class of similar products) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Nov. 28, 2021	Nov. 29, 2020	Nov. 28, 2021	Nov. 29, 2020
Product Information [Line Items]
Net sales	$ 5,024.0	$ 4,719.4	$ 9,563.9	$ 9,083.4
Snacks [Member]
Product Information [Line Items]
Net sales	947.6	845.0	1,902.1	1,736.7
Convenient meals [Member]
Product Information [Line Items]
Net sales	789.8	820.2	1,485.3	1,549.8
Cereal [Member]
Product Information [Line Items]
Net sales	742.2	701.4	1,473.2	1,453.3
Pet [Member]
Product Information [Line Items]
Net sales	593.4	460.0	1,081.4	851.7
Yogurt [Member]
Product Information [Line Items]
Net sales	507.1	520.2	1,013.0	1,008.2
Dough [Member]
Product Information [Line Items]
Net sales	607.0	574.5	1,012.2	958.8
Baking mixes and ingredients [Member]
Product Information [Line Items]
Net sales	517.2	478.8	913.5	876.8
Super-premium ice cream [Member]
Product Information [Line Items]
Net sales	200.0	199.5	444.8	432.4
Other [Member]
Product Information [Line Items]
Net sales	$ 119.7	$ 119.8	$ 238.4	$ 215.7