Fair Value Measurements - Fair Value Hierarchy (Details) - USD ($) $ in Millions	Feb. 27, 2021	May 30, 2020
Mutual funds - equity
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - equity	$ 0.7	$ 0.7
Mutual funds - fixed income
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - fixed income	6.8	6.3
NAV | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - equity	0.0	0.0
Deferred compensation plan	0.0	0.0
Total	201.8	283.7
Foreign currency forward contracts - liability	0.0	0.0
Total	0.0	0.0
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Deferred compensation plan	14.8	13.2
Total	16.7	15.0
Total	0.2	0.8
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring | Foreign currency forward contracts
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Foreign currency forward contracts - liability	0.2	0.8
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring | Other Assets
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - fixed income	6.8	6.3
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring | Other Liabilities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - fixed income	14.7	25.0
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring | Other Liabilities | Interest rate swap agreement
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Interest rate swap agreement - liability	14.7	25.0
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring | Other Current Assets [Member] | Foreign currency forward contracts
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Foreign currency forward contracts - asset	1.2	1.1
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring | Mutual funds - equity
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - equity	0.7	0.7
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring | Mutual funds - fixed income
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - fixed income	6.8	6.3
Money market funds | NAV | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Money market funds	201.8	283.7
Money market funds | Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Money market funds	$ 0.0	$ 0.0