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Fair Value of Financial Instruments - Schedule of Fair Value Assets and Liabilities Measured on a Recurring and Nonrecurring Basis (Details) - USD ($) $ in Millions	Jun. 02, 2018	Jun. 03, 2017
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale marketable securities	$ 8.6	$ 8.6
Fair Value, Measurements, Recurring [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Total	160.1	25.2
Fair Value, Measurements, Recurring [Member] | Quoted Prices With Other Observable Inputs (Level 2)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Cash Equivalents	121.0	0.0
Deferred Compensation Plan	15.1	12.8
Contingent consideration	0.0	0.0
Total	0.3	0.6
Fair Value, Measurements, Recurring [Member] | Fair Value, Inputs, Level 3 [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Cash Equivalents	0.0	0.0
Deferred Compensation Plan	0.0	0.0
Total	0.0	0.0
Contingent consideration	0.5	0.5
Total	0.5	0.5
Mutual funds - fixed income
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale marketable securities	7.7	7.7
Mutual funds - fixed income | Fair Value, Measurements, Recurring [Member] | Quoted Prices With Other Observable Inputs (Level 2)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale marketable securities	7.7	7.7
Mutual funds - fixed income | Fair Value, Measurements, Recurring [Member] | Fair Value, Inputs, Level 3 [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale marketable securities	0.0	0.0
Mutual funds - equity
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale marketable securities	0.9	0.9
Mutual funds - equity | Fair Value, Measurements, Recurring [Member] | Quoted Prices With Other Observable Inputs (Level 2)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale marketable securities	0.9	0.9
Mutual funds - equity | Fair Value, Measurements, Recurring [Member] | Fair Value, Inputs, Level 3 [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale marketable securities	0.0	0.0
Interest Rate Swap | Fair Value, Measurements, Recurring [Member] | Quoted Prices With Other Observable Inputs (Level 2)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Interest Rate Swap Agreement		3.3
Interest Rate Swap | Fair Value, Measurements, Recurring [Member] | Fair Value, Inputs, Level 3 [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Interest Rate Swap Agreement	0.0	0.0
Foreign currency forward contracts | Fair Value, Measurements, Recurring [Member] | Quoted Prices With Other Observable Inputs (Level 2)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Foreign currency forward contracts	0.4	0.5
Foreign currency forward contracts	0.3	0.6
Foreign currency forward contracts | Fair Value, Measurements, Recurring [Member] | Fair Value, Inputs, Level 3 [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Foreign currency forward contracts	0.0	0.0
Foreign currency forward contracts	$ 0.0	$ 0.0

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- Definition

Fair value portion of probable future economic benefits obtained or controlled by an entity as a result of past transactions or events.

+ References

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-Publisher FASB
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Amount of investment in debt and equity securities categorized neither as held-to-maturity nor trading.

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Amount of liability recognized arising from contingent consideration in a business combination.

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Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
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-SubTopic 30
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Fair value portion of currency on hand as well as demand deposits with banks or financial institutions. Includes other kinds of accounts that have the general characteristics of demand deposits. Also includes short-term, highly liquid investments that are both readily convertible to known amounts of cash and so near their maturity that they present insignificant risk of changes in value because of changes in interest rates.

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Carrying amount as of the balance sheet date of assets held under deferred compensation agreements.

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-Publisher FASB
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Fair value as of the balance sheet date of all interest rate derivative assets designated as cash flow hedging instruments.

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Fair value of financial and nonfinancial obligations.

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