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CONSOLIDATED STATEMENTS OF CASH FLOWS (Unaudited) - USD ($)
$ in Millions
 3 Months Ended
Nov. 30, 2024
Nov. 30, 2023
Cash flows from operating activities:    
Net income $ 106.7 $ 100.6
Adjustments to reconcile net income to cash flows from operating activities:    
Depreciation and amortization 21.6 22.7
Share-based payment expense 12.1 11.1
Changes in operating assets and liabilities, net of acquisitions and divestitures:    
Accounts receivable 25.2 37.8
Inventories (5.1) 3.2
Prepayments and other current assets (1.8) (5.3)
Accounts payable (14.5) 28.7
Other operating activities (12.0) (8.8)
Net cash provided by operating activities 132.2 190.0
Cash flows from investing activities:    
Purchases of property, plant, and equipment (18.9) (14.6)
Other investing activities 0.5 0.1
Net cash used for investing activities (18.4) (14.5)
Cash flows from financing activities:    
Repurchases of common stock (6.7) (48.2)
Proceeds from stock option exercises and other 15.6 1.6
Payments of taxes withheld on net settlement of equity awards (23.1) (9.0)
Dividends paid (4.5) (4.1)
Net cash used for financing activities (18.7) (59.7)
Effect of exchange rate changes on cash and cash equivalents (5.3) (0.4)
Net change in cash and cash equivalents 89.8 115.4
Cash and cash equivalents at beginning of period 845.8 397.9
Cash and cash equivalents at end of period 935.6 513.3
Supplemental cash flow information:    
Income taxes paid during the period 9.6 7.1
Interest paid during the period $ 11.6 $ 12.8