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Consolidated Statements of Cash Flows - USD ($)
$ in Millions
 12 Months Ended
Aug. 31, 2024
Aug. 31, 2023
Aug. 31, 2022
Cash flows from operating activities:      
Net income $ 422.6 $ 346.0 $ 384.0
Adjustments to reconcile net income to cash flows from operating activities:      
Depreciation and amortization 91.1 93.2 94.8
Share-based payment expense 46.6 42.0 37.4
Gain on the sale or disposal of property, plant, and equipment 0.0 0.0 (2.3)
Asset impairments 3.0 20.8 1.7
Loss on sale of a business 0.0 11.2 0.0
Deferred income taxes (33.6) (47.8) 0.6
Changes in operating assets and liabilities, net of acquisitions and divestitures:      
Accounts receivable (8.7) 114.6 (99.7)
Inventories (16.3) 115.2 (83.3)
Prepayments and other current assets (3.0) 21.4 (17.6)
Accounts payable 66.2 (110.5) 2.6
Other operating activities 51.3 (28.0) (1.9)
Net cash provided by operating activities 619.2 578.1 316.3
Cash flows from investing activities:      
Purchases of property, plant, and equipment (64.0) (66.7) (56.5)
Proceeds from sale of property, plant, and equipment 0.0 0.0 8.9
Acquisitions of businesses, net of cash acquired 0.0 (35.5) (12.9)
Other investing activities (1.1) 11.5 (1.7)
Net cash used for investing activities (65.1) (90.7) (62.2)
Cash flows from financing activities:      
Repayments on credit facility, net of borrowings 0.0 (18.0) 18.0
Repurchases of common stock (88.7) (266.6) (514.8)
Proceeds from stock option exercises and other 13.5 2.7 12.5
Payments of taxes withheld on net settlement of equity awards (11.1) (14.2) (8.6)
Dividends paid (18.2) (16.8) (18.1)
Other financing activities 0.0 0.0 (1.4)
Net cash used for financing activities (104.5) (312.9) (512.4)
Effect of exchange rate changes on cash and cash equivalents (1.7) 0.2 (9.8)
Net change in cash and cash equivalents 447.9 174.7 (268.1)
Cash and cash equivalents at beginning of year 397.9 223.2 491.3
Cash and cash equivalents at end of year 845.8 397.9 223.2
Supplemental cash flow information:      
Income taxes paid 155.7 147.2 109.4
Interest paid $ 24.4 $ 27.9 $ 26.1