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Consolidated Statements of Cash Flows (Unaudited) - USD ($)
$ in Millions
 3 Months Ended
Nov. 30, 2019
Nov. 30, 2018
Cash flows from operating activities:    
Net income $ 57.0 $ 79.6
Adjustments to reconcile net income to net cash flows from operating activities:    
Depreciation and amortization 24.2 21.3
Share-based payment expense 16.7 7.8
Loss on sale or disposal of property, plant, and equipment 0.1 0.4
Deferred income taxes 0.4 (0.1)
Change in assets and liabilities, net of effect of acquisitions, divestitures, and exchange rate changes:    
Accounts receivable 66.3 102.0
Inventories 4.9 (9.2)
Prepayments and other current assets (3.3) (14.8)
Accounts payable (22.7) (61.5)
Other current liabilities (28.3) (1.6)
Other 14.3 7.9
Net cash provided by operating activities 129.6 131.8
Cash flows from investing activities:    
Purchases of property, plant, and equipment (11.6) (14.0)
Acquisition of businesses, net of cash acquired (302.0) 0.0
Other investing activities (1.5) 2.7
Net cash used for investing activities (315.1) (11.3)
Cash flows from financing activities:    
Borrowings on credit facility 0.0 55.4
Repayments of borrowings on credit facility 0.0 (55.4)
Repayments of long-term debt (0.4) (0.1)
Repurchases of common stock 0.0 (25.0)
Proceeds from stock option exercises and other 0.2 0.1
Payments of taxes withheld on net settlement of equity awards (4.1) (3.9)
Dividends paid (5.2) (5.2)
Net cash used for financing activities (9.5) (34.1)
Effect of exchange rate changes on cash and cash equivalents 0.6 (0.7)
Net change in cash and cash equivalents (194.4) 85.7
Cash and cash equivalents at beginning of period 461.0 129.1
Cash and cash equivalents at end of period 266.6 214.8
Supplemental cash flow information:    
Income taxes paid during the period 4.6 6.1
Interest paid during the period $ 12.9 $ 13.5