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Fair Value Measurements - Fair Value Hierarchy (Details) - USD ($) $ in Millions	Mar. 02, 2019	Jun. 02, 2018
Mutual funds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - equity	$ 0.9	$ 0.9
Fixed Income Securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale Securities	8.0	7.7
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Deferred compensation plan	15.9	15.1
Total	17.5	16.4
Contingent consideration	0.0	0.0
Total	0.3	0.3
Available-for-sale Securities	18.0	22.7
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring | Interest rate swap agreement
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale Securities	10.0	15.0
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring | Foreign Exchange Forward
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Foreign currency forward contracts	0.7	0.4
Foreign currency forward contracts	0.3	0.3
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring | Mutual funds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - equity	0.9	0.9
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring | Fixed Income Securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale Securities	8.0	7.7
Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Deferred compensation plan	0.0	0.0
Total	0.0	0.0
Contingent consideration	0.4	0.5
Total	0.4	0.5
Available-for-sale Securities	0.0	0.0
Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring | Interest rate swap agreement
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale Securities	0.0	0.0
Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring | Foreign Exchange Forward
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Foreign currency forward contracts	0.0	0.0
Foreign currency forward contracts	0.0	0.0
Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring | Mutual funds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - equity	0.0	0.0
Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring | Fixed Income Securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale Securities	0.0	0.0
Money market funds | NAV | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Cash equivalents	31.0	121.0
Money market funds | Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Cash equivalents	$ 0.0	$ 0.0

X

- 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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-Topic 820
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Amount of investment in debt and equity securities categorized neither as held-to-maturity nor trading.

+ References

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- Definition

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

+ References

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-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-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.

+ References

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-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
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Amount of investment in equity security measured at fair value with change in fair value recognized in net income (FV-NI).

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Fair value portion of asset contracts related to the exchange of different currencies, including, but not limited to, foreign currency options, forward contracts, and swaps.

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Fair value of financial and nonfinancial obligations.

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