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CONSOLIDATED STATEMENTS OF CASH FLOWS (Unaudited) - USD ($)
$ in Millions
 9 Months Ended
May 31, 2023
May 31, 2022
Cash flows from operating activities:    
Net income $ 263.1 $ 268.6
Adjustments to reconcile net income to net cash flows from operating activities:    
Depreciation and amortization 70.4 71.4
Share-based payment expense 32.4 27.5
Gain on sale of property, plant, and equipment 0.0 (2.3)
Asset impairment 4.3 1.7
Loss on sale of a business 11.2 0.0
Changes in operating assets and liabilities, net of acquisitions and divestitures:    
Accounts receivable 123.9 (27.2)
Inventories 82.6 (174.5)
Prepayments and other current assets (9.6) (38.3)
Accounts payable (53.4) 58.9
Other (53.4) (20.1)
Net cash provided by operating activities 471.5 165.7
Cash flows from investing activities:    
Purchases of property, plant, and equipment (48.0) (38.0)
Proceeds from sale of property, plant, and equipment 0.0 8.9
Acquisition of businesses, net of cash acquired (35.4) (12.2)
Other investing activities 7.0 (1.9)
Net cash used for investing activities (76.4) (43.2)
Cash flows from financing activities:    
Repayments on credit facility, net of borrowings (18.0) 122.0
Repurchases of common stock (216.2) (403.5)
Proceeds from stock option exercises and other 2.1 10.6
Payments of taxes withheld on net settlement of equity awards (13.9) (8.0)
Dividends paid (12.7) (13.7)
Net cash used for financing activities (258.7) (292.6)
Effect of exchange rate changes on cash and cash equivalents (0.3) (3.0)
Net change in cash and cash equivalents 136.1 (173.1)
Cash and cash equivalents at beginning of period 223.2 491.3
Cash and cash equivalents at end of period 359.3 318.2
Supplemental cash flow information:    
Income taxes paid during the period 83.8 80.8
Interest paid during the period $ 22.3 $ 19.2