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Income Taxes - Effective Income Tax Rate Reconciliation (Details) - USD ($) $ in Millions	12 Months Ended
	Jun. 02, 2018	Jun. 03, 2017	May 28, 2016
Income Tax Disclosure [Abstract]
Income taxes computed at the United States Statutory rate	$ 49.0	$ 62.2	$ 68.8
Remeasurement of U.S. deferred tax assets and liabilities due to the Tax Act	(8.9)	0.0	0.0
Foreign statutory rate differences	(4.0)	(5.7)	(4.3)
Manufacturing deduction under the American Jobs Creation Act of 2004	2.7	3.4	4.8
State taxes	3.3	3.8	5.2
Tax on undistributed foreign earnings	9.0	0.0	0.0
United Kingdom patent box deduction for research and development	(1.8)	(2.6)	(1.7)
Research and development credit	(2.4)	(1.4)	(1.4)
Sale of manufacturing facility in the United Kingdom	0.0	0.0	(1.6)
Other, net	0.9	2.2	(0.7)
Income tax expense	$ 42.4	$ 55.1	$ 59.5
Effective tax rate	25.20%	31.10%	30.30%

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Income Tax Reconciliation, Tax Cuts and Jobs Act of 2017

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