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Supplemental Guarantor Condensed Consolidating Financial Statements (Income) (Details) - USD ($)
$ in Millions
 3 Months Ended
Nov. 30, 2018
Nov. 30, 2017
Condensed Financial Statements, Captions [Line Items]    
Total sales $ 932.6 $ 842.8
Cost of products sold 565.1 492.9
Gross profit 367.5 349.9
Selling, distribution, and administrative expenses 250.1 229.5
Intercompany charges 0.0 0.0
Special charge 1.0 0.2
Operating profit 116.4 120.2
Interest expense, net 8.7 8.1
Equity earnings in subsidiaries 0.0 0.0
Miscellaneous expense (income), net 1.3 1.2
Income before income taxes 106.4 110.9
Income tax (benefit) expense 26.8 39.4
Net income 79.6 71.5
Other comprehensive income (loss) items:    
Foreign currency translation adjustments (8.8) (10.5)
Defined benefit pension plans, net 2.6 1.6
Other comprehensive loss, net of tax (6.2) (8.9)
Comprehensive income 73.4 62.6
Parent    
Condensed Financial Statements, Captions [Line Items]    
Total sales 0.0 0.0
Cost of products sold 0.0 0.0
Gross profit 0.0 0.0
Selling, distribution, and administrative expenses 8.9 11.1
Intercompany charges (1.3) (1.0)
Special charge 0.0 0.0
Operating profit (7.6) (10.1)
Interest expense, net 3.1 2.7
Equity earnings in subsidiaries (89.2) (80.9)
Miscellaneous expense (income), net 1.9 1.6
Income before income taxes 76.6 66.5
Income tax (benefit) expense (3.0) (5.0)
Net income 79.6 71.5
Other comprehensive income (loss) items:    
Foreign currency translation adjustments (8.8) (10.5)
Defined benefit pension plans, net 2.6 1.6
Other comprehensive loss, net of tax (6.2) (8.9)
Comprehensive income 73.4 62.6
Subsidiary Issuer    
Condensed Financial Statements, Captions [Line Items]    
Total sales 828.9 744.2
Cost of products sold 500.5 430.1
Gross profit 328.4 314.1
Selling, distribution, and administrative expenses 217.7 194.7
Intercompany charges 0.0 (0.5)
Special charge 1.0 0.2
Operating profit 109.7 119.7
Interest expense, net 4.4 4.0
Equity earnings in subsidiaries (3.3) (1.1)
Miscellaneous expense (income), net (0.6) 0.5
Income before income taxes 109.2 116.3
Income tax (benefit) expense 26.6 42.2
Net income 82.6 74.1
Other comprehensive income (loss) items:    
Foreign currency translation adjustments (8.8) (10.5)
Defined benefit pension plans, net 1.2 1.2
Other comprehensive loss, net of tax (7.6) (9.3)
Comprehensive income 75.0 64.8
Subsidiary Guarantor    
Condensed Financial Statements, Captions [Line Items]    
Total sales 13.7 12.0
Cost of products sold 0.0 0.0
Gross profit 13.7 12.0
Selling, distribution, and administrative expenses 0.7 0.8
Intercompany charges 0.0 0.0
Special charge 0.0 0.0
Operating profit 13.0 11.2
Interest expense, net 0.0 0.0
Equity earnings in subsidiaries 0.0 0.0
Miscellaneous expense (income), net 0.0 0.0
Income before income taxes 13.0 11.2
Income tax (benefit) expense 2.7 2.2
Net income 10.3 9.0
Other comprehensive income (loss) items:    
Foreign currency translation adjustments 0.0 0.0
Defined benefit pension plans, net 0.0 0.0
Other comprehensive loss, net of tax 0.0 0.0
Comprehensive income 10.3 9.0
Non- Guarantors    
Condensed Financial Statements, Captions [Line Items]    
Total sales 156.7 142.1
Cost of products sold 116.3 104.9
Gross profit 40.4 37.2
Selling, distribution, and administrative expenses 37.8 36.3
Intercompany charges 1.3 1.5
Special charge 0.0 0.0
Operating profit 1.3 (0.6)
Interest expense, net 1.2 1.4
Equity earnings in subsidiaries 0.1 0.0
Miscellaneous expense (income), net 0.0 (0.9)
Income before income taxes 0.0 (1.1)
Income tax (benefit) expense 0.5 0.0
Net income (0.5) (1.1)
Other comprehensive income (loss) items:    
Foreign currency translation adjustments 0.0 0.0
Defined benefit pension plans, net 0.3 0.4
Other comprehensive loss, net of tax 0.3 0.4
Comprehensive income (0.2) (0.7)
Consolidating Adjustments    
Condensed Financial Statements, Captions [Line Items]    
Total sales (66.7) (55.5)
Cost of products sold (51.7) (42.1)
Gross profit (15.0) (13.4)
Selling, distribution, and administrative expenses (15.0) (13.4)
Intercompany charges 0.0 0.0
Special charge 0.0 0.0
Operating profit 0.0 0.0
Interest expense, net 0.0 0.0
Equity earnings in subsidiaries 92.4 82.0
Miscellaneous expense (income), net 0.0 0.0
Income before income taxes (92.4) (82.0)
Income tax (benefit) expense 0.0 0.0
Net income (92.4) (82.0)
Other comprehensive income (loss) items:    
Foreign currency translation adjustments 8.8 10.5
Defined benefit pension plans, net (1.5) (1.6)
Other comprehensive loss, net of tax 7.3 8.9
Comprehensive income (85.1) (73.1)
External Customer [Member]    
Condensed Financial Statements, Captions [Line Items]    
Total sales 932.6 842.8
External Customer [Member] | Parent    
Condensed Financial Statements, Captions [Line Items]    
Total sales 0.0 0.0
External Customer [Member] | Subsidiary Issuer    
Condensed Financial Statements, Captions [Line Items]    
Total sales 828.9 744.2
External Customer [Member] | Subsidiary Guarantor    
Condensed Financial Statements, Captions [Line Items]    
Total sales 0.0 0.0
External Customer [Member] | Non- Guarantors    
Condensed Financial Statements, Captions [Line Items]    
Total sales 103.7 98.6
External Customer [Member] | Consolidating Adjustments    
Condensed Financial Statements, Captions [Line Items]    
Total sales 0.0 0.0
Inter-Company [Member]    
Condensed Financial Statements, Captions [Line Items]    
Total sales 0.0 0.0
Inter-Company [Member] | Consolidating Adjustments    
Condensed Financial Statements, Captions [Line Items]    
Total sales (66.7) (55.5)
Inter-Company [Member] | Consolidating Adjustments | Parent    
Condensed Financial Statements, Captions [Line Items]    
Total sales 0.0 0.0
Inter-Company [Member] | Consolidating Adjustments | Subsidiary Issuer    
Condensed Financial Statements, Captions [Line Items]    
Total sales 0.0 0.0
Inter-Company [Member] | Consolidating Adjustments | Subsidiary Guarantor    
Condensed Financial Statements, Captions [Line Items]    
Total sales 13.7 12.0
Inter-Company [Member] | Consolidating Adjustments | Non- Guarantors    
Condensed Financial Statements, Captions [Line Items]    
Total sales $ 53.0 $ 43.5