Fair Value Measurements - Fair Value Hierarchy (Details) - USD ($) $ in Millions	Dec. 02, 2017	Jun. 03, 2017
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale marketable securities	$ 8.5	$ 8.6
Fixed Income Securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale marketable securities	7.6	7.7
Mutual funds - equity
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale marketable securities	0.9	0.9
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	14.3	12.8
Total	28.4	25.2
Contingent consideration	0.0	0.0
Total	0.9	0.6
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	0.4	0.5
Foreign currency forward contracts	0.5	0.6
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring | Interest Rate Swap
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Interest rate swap agreement	5.2	3.3
Interest rate swap agreement	0.4	0.0
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 marketable securities	7.6	7.7
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring | Mutual funds - equity
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale marketable securities	0.9	0.9
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	0.5	0.5
Total	0.5	0.5
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 | Interest Rate Swap
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Interest rate swap agreement	0.0	0.0
Interest rate swap agreement	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 marketable securities	0.0	0.0
Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring | Mutual funds - equity
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale marketable securities	$ 0.0	$ 0.0