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Income Taxes - Effective Income Tax Rate Reconciliation (Details) - USD ($) $ in Millions | 12 Months Ended
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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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