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Supplemental Guarantor Condensed Consolidating Financial Statements - Cash Flows (Details) - USD ($)
$ in Millions
 12 Months Ended
Aug. 31, 2019
Aug. 31, 2018
Aug. 31, 2017
Condensed Financial Statements of Cash Flows      
Net cash provided by operating activities $ 494.7 $ 351.5 $ 336.6
Cash flows from investing activities:      
Purchases of property, plant, and equipment (53.0) (43.6) (67.3)
Proceeds from sale of property, plant, and equipment 0.0 0.0 5.5
Investments in subsidiaries 0.0 0.0  
Acquisitions of businesses and intangible assets (2.9) (163.2) 0.0
Proceeds from sale of business 0.0 1.1 0.0
Proceeds from sale of investment in unconsolidated affiliate 0.0 0.0 13.2
Other investing activities 2.9 1.7 (0.2)
Net cash used for investing activities (53.0) (204.0) (48.8)
Cash flow from financing activities:      
Borrowings on credit facility 86.5 395.4 0.0
Repayments of borrowings on credit facility (86.5) (395.4) 0.0
(Repayments) issuances of long-term debt (0.4) (0.4)  
(Repayments) issuances of long-term debt     1.0
Proceeds from stock option exercises and other 0.6 1.7 3.0
Repurchases of common stock (81.6) (298.4) (357.9)
Withholding taxes on net settlement of equity awards (6.0) (8.2) (15.2)
Intercompany dividends   0.0  
Intercompany capital   0.0  
Dividends paid (20.8) (21.4) (22.7)
Net cash used for financing activities (108.2) (326.7) (391.8)
Effect of exchange rate changes on cash (1.6) (2.8) 1.9
Net change in cash and cash equivalents 331.9 (182.0) (102.1)
Cash and cash equivalents at beginning of year 129.1 311.1 413.2
Cash and cash equivalents at end of year 461.0 129.1 311.1
Consolidating Adjustments      
Condensed Financial Statements of Cash Flows      
Net cash provided by operating activities (2.9) (36.8) 0.0
Cash flows from investing activities:      
Purchases of property, plant, and equipment 0.0 0.0 0.0
Proceeds from sale of property, plant, and equipment     0.0
Investments in subsidiaries 2.9 154.7  
Acquisitions of businesses and intangible assets 0.0 0.0  
Proceeds from sale of business   0.0  
Proceeds from sale of investment in unconsolidated affiliate     0.0
Other investing activities 0.0 0.0 0.0
Net cash used for investing activities 2.9 154.7 0.0
Cash flow from financing activities:      
Borrowings on credit facility 0.0 0.0  
Repayments of borrowings on credit facility 0.0 0.0  
(Repayments) issuances of long-term debt 0.0 0.0  
(Repayments) issuances of long-term debt     0.0
Proceeds from stock option exercises and other 0.0 0.0 0.0
Repurchases of common stock 0.0 0.0 0.0
Withholding taxes on net settlement of equity awards 0.0 0.0 0.0
Intercompany dividends   36.8  
Intercompany capital   (154.7)  
Dividends paid 0.0 0.0 0.0
Net cash used for financing activities 0.0 (117.9) 0.0
Effect of exchange rate changes on cash 0.0 0.0 0.0
Net change in cash and cash equivalents 0.0 0.0 0.0
Cash and cash equivalents at beginning of year 0.0 0.0 0.0
Cash and cash equivalents at end of year 0.0 0.0 0.0
Parent      
Condensed Financial Statements of Cash Flows      
Net cash provided by operating activities 391.1 322.1 262.3
Cash flows from investing activities:      
Purchases of property, plant, and equipment 0.0 0.0 0.0
Proceeds from sale of property, plant, and equipment     0.0
Investments in subsidiaries (2.9) (154.7)  
Acquisitions of businesses and intangible assets 0.0 0.0  
Proceeds from sale of business   0.0  
Proceeds from sale of investment in unconsolidated affiliate     0.0
Other investing activities 0.8 1.7 0.0
Net cash used for investing activities (2.1) (153.0) 0.0
Cash flow from financing activities:      
Borrowings on credit facility 0.0 0.0  
Repayments of borrowings on credit facility 0.0 0.0  
(Repayments) issuances of long-term debt 0.0 0.0  
(Repayments) issuances of long-term debt     0.0
Proceeds from stock option exercises and other 0.6 1.7 3.0
Repurchases of common stock (81.6) (298.4) (357.9)
Withholding taxes on net settlement of equity awards (6.0) (8.2) (15.2)
Intercompany dividends   0.0  
Intercompany capital   0.0  
Dividends paid (20.8) (21.4) (22.7)
Net cash used for financing activities (107.8) (326.3) (392.8)
Effect of exchange rate changes on cash 0.2 0.0 0.0
Net change in cash and cash equivalents 281.4 (157.2) (130.5)
Cash and cash equivalents at beginning of year 80.5 237.7 368.2
Cash and cash equivalents at end of year 361.9 80.5 237.7
Subsidiary Issuer      
Condensed Financial Statements of Cash Flows      
Net cash provided by operating activities 63.4 30.2 41.4
Cash flows from investing activities:      
Purchases of property, plant, and equipment (44.5) (31.4) (53.1)
Proceeds from sale of property, plant, and equipment     0.2
Investments in subsidiaries 0.0 0.0  
Acquisitions of businesses and intangible assets (2.9) (136.3)  
Proceeds from sale of business   0.0  
Proceeds from sale of investment in unconsolidated affiliate     13.2
Other investing activities 2.1 0.0 (0.2)
Net cash used for investing activities (45.3) (167.7) (39.9)
Cash flow from financing activities:      
Borrowings on credit facility 86.5 395.4  
Repayments of borrowings on credit facility (86.5) (395.4)  
(Repayments) issuances of long-term debt 0.0 0.0  
(Repayments) issuances of long-term debt     0.0
Proceeds from stock option exercises and other 0.0 0.0 0.0
Repurchases of common stock 0.0 0.0 0.0
Withholding taxes on net settlement of equity awards 0.0 0.0 0.0
Intercompany dividends   0.0  
Intercompany capital   136.6  
Dividends paid 0.0 0.0 0.0
Net cash used for financing activities 0.0 136.6 0.0
Effect of exchange rate changes on cash 0.0 0.9 (1.5)
Net change in cash and cash equivalents 18.1 0.0 0.0
Cash and cash equivalents at beginning of year 0.0 0.0 0.0
Cash and cash equivalents at end of year 18.1 0.0 0.0
Subsidiary Guarantor      
Condensed Financial Statements of Cash Flows      
Net cash provided by operating activities 0.0 0.0 0.0
Cash flows from investing activities:      
Purchases of property, plant, and equipment 0.0 0.0 0.0
Proceeds from sale of property, plant, and equipment     0.0
Investments in subsidiaries 0.0 0.0  
Acquisitions of businesses and intangible assets 0.0 0.0  
Proceeds from sale of business   0.0  
Proceeds from sale of investment in unconsolidated affiliate     0.0
Other investing activities 0.0 0.0 0.0
Net cash used for investing activities 0.0 0.0 0.0
Cash flow from financing activities:      
Borrowings on credit facility 0.0 0.0  
Repayments of borrowings on credit facility 0.0 0.0  
(Repayments) issuances of long-term debt 0.0 0.0  
(Repayments) issuances of long-term debt     0.0
Proceeds from stock option exercises and other 0.0 0.0 0.0
Repurchases of common stock 0.0 0.0 0.0
Withholding taxes on net settlement of equity awards 0.0 0.0 0.0
Intercompany dividends   0.0  
Intercompany capital   0.0  
Dividends paid 0.0 0.0 0.0
Net cash used for financing activities 0.0 0.0 0.0
Effect of exchange rate changes on cash 0.0 0.0 0.0
Net change in cash and cash equivalents 0.0 0.0 0.0
Cash and cash equivalents at beginning of year 0.0 0.0 0.0
Cash and cash equivalents at end of year 0.0 0.0 0.0
Non- Guarantors      
Condensed Financial Statements of Cash Flows      
Net cash provided by operating activities 43.1 36.0 32.9
Cash flows from investing activities:      
Purchases of property, plant, and equipment (8.5) (12.2) (14.2)
Proceeds from sale of property, plant, and equipment     5.3
Investments in subsidiaries 0.0 0.0  
Acquisitions of businesses and intangible assets 0.0 (26.9)  
Proceeds from sale of business   1.1  
Proceeds from sale of investment in unconsolidated affiliate     0.0
Other investing activities 0.0 0.0 0.0
Net cash used for investing activities (8.5) (38.0) (8.9)
Cash flow from financing activities:      
Borrowings on credit facility 0.0 0.0  
Repayments of borrowings on credit facility 0.0 0.0  
(Repayments) issuances of long-term debt (0.4) (0.4)  
(Repayments) issuances of long-term debt     1.0
Proceeds from stock option exercises and other 0.0 0.0 0.0
Repurchases of common stock 0.0 0.0 0.0
Withholding taxes on net settlement of equity awards 0.0 0.0 0.0
Intercompany dividends   (36.8)  
Intercompany capital   18.1  
Dividends paid 0.0 0.0 0.0
Net cash used for financing activities (0.4) (19.1) 1.0
Effect of exchange rate changes on cash (1.8) (3.7) 3.4
Net change in cash and cash equivalents 32.4 (24.8) 28.4
Cash and cash equivalents at beginning of year 48.6 73.4 45.0
Cash and cash equivalents at end of year $ 81.0 $ 48.6 $ 73.4