Income Taxes - Components of Income Tax Expense (Benefit) (Details) - USD ($) $ in Millions	12 Months Ended
	Jun. 01, 2019	Jun. 02, 2018	Jun. 03, 2017
Income Tax Disclosure [Abstract]
Current: Domestic - Federal	$ 19.0	$ 30.2	$ 28.7
Domestic - State	6.4	4.3	2.3
Foreign	12.9	10.7	11.1
Current Income Tax Expense (Benefit)	38.3	45.2	42.1
Deferred: Domestic - Federal	1.0	(4.1)	9.2
Domestic - State	(0.2)	0.1	2.8
Foreign	0.5	1.2	1.0
Deferred Income Tax Expense (Benefit)	1.3	(2.8)	13.0
Income tax expense	$ 39.6	$ 42.4	$ 55.1