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Income Taxes - Effective Income Tax Rate Reconciliation (Details) - USD ($) $ in Millions	12 Months Ended
	Jun. 01, 2019	Jun. 02, 2018	Jun. 03, 2017
Income Tax Disclosure [Abstract]
Income taxes computed at the United States Statutory rate	$ 41.0	$ 49.0	$ 62.2
Remeasurement of U.S. deferred tax assets and liabilities due to the Tax Act	(0.2)	(8.9)	0.0
U.S. tax liability on undistributed foreign earnings due to the Tax Act	(2.6)	9.0	0.0
Foreign-derived intangible income	(3.1)
Global intangible low-taxed income	6.9
Foreign statutory rate differences	1.9	(4.0)	(5.7)
Manufacturing deduction under the American Jobs Creation Act of 2004	0.0	(2.7)	(3.4)
State taxes	4.9	3.3	3.8
United Kingdom patent box deduction for research and development	(1.9)	(1.8)	(2.6)
Research and development credit	(3.4)	(2.4)	(1.4)
Foreign tax credit	(5.7)	(2.4)	(0.6)
Other, net	1.8	3.3	2.8
Income tax expense	$ 39.6	$ 42.4	$ 55.1
Effective tax rate	20.30%	25.20%	31.10%

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