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CONSOLIDATED STATEMENTS OF CASH FLOWS (Unaudited) - USD ($)
$ in Millions
 3 Months Ended
Nov. 30, 2022
Nov. 30, 2021
Cash flows from operating activities:    
Net income $ 74.9 $ 87.6
Adjustments to reconcile net income to net cash flows from operating activities:    
Depreciation and amortization 26.5 24.3
Share-based payment expense 10.7 7.6
Asset impairment 4.3 0.0
Loss on sale of a business 11.2 0.0
Changes in operating assets and liabilities, net of acquisitions and divestitures:    
Accounts receivable 81.6 40.2
Inventories (5.8) (41.3)
Prepayments and other current assets (8.5) (47.7)
Accounts payable 20.3 17.7
Other (28.6) (4.7)
Net cash provided by operating activities 186.6 83.7
Cash flows from investing activities:    
Purchases of property, plant, and equipment (18.2) (9.3)
Other investing activities 3.9 0.3
Net cash used for investing activities (14.3) (9.0)
Cash flows from financing activities:    
Repayments on credit facility, net of borrowings (18.0) 0.0
Repurchases of common stock (76.5) (56.3)
Proceeds from stock option exercises and other 0.9 8.6
Payments of taxes withheld on net settlement of equity awards (12.5) (6.7)
Dividends paid (4.3) (4.7)
Net cash used for financing activities (110.4) (59.1)
Effect of exchange rate changes on cash and cash equivalents (1.0) (2.9)
Net change in cash and cash equivalents 60.9 12.7
Cash and cash equivalents at beginning of period 223.2 491.3
Cash and cash equivalents at end of period 284.1 504.0
Supplemental cash flow information:    
Income taxes paid during the period 11.0 28.3
Interest paid during the period $ 15.3 $ 13.3