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Income Taxes - Effective Income Tax Rate Reconciliation (Details) - USD ($) $ in Millions	12 Months Ended
	Jun. 03, 2017	May 28, 2016	May 30, 2015
Income Tax Disclosure [Abstract]
Income taxes computed at the United States Statutory rate of 35%	$ 62.2	$ 68.8	$ 50.8
Foreign statutory rate differences	(5.7)	(4.3)	(1.0)
Manufacturing deduction under the American Jobs Creation Act of 2004	3.4	4.8	4.8
State taxes	3.8	5.2	4.2
Tax on undistributed foreign earnings	0.0	0.0	(3.9)
United Kingdom patent box deduction for research and development	(2.6)	(1.7)	(0.3)
Sale of manufacturing facility in the United Kingdom	0.0	(1.6)	0.0
Other, net	0.8	(2.1)	2.2
Income tax expense	$ 55.1	$ 59.5	$ 47.2
Effective tax rate	31.10%	30.30%	32.60%

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