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Consolidated Statements of Cash Flows - USD ($)
$ in Millions
 12 Months Ended
Aug. 31, 2022
Aug. 31, 2021
Aug. 31, 2020
Cash flows from operating activities:      
Net income $ 384.0 $ 306.3 $ 248.3
Adjustments to reconcile net income to cash flows from operating activities      
Depreciation and amortization 94.8 100.1 101.1
Share-based payment expense 37.4 32.5 38.2
(Gain) loss on the sale or disposal of property, plant, and equipment (2.3) (0.1) 0.3
Asset impairments 1.7 6.0 8.8
Deferred income taxes 0.6 (2.7) (6.7)
Changes in operating assets and liabilities, net of acquisitions      
Accounts receivable (99.7) (68.7) 74.5
Inventories (83.3) (35.5) 38.0
Prepayments and other current assets (17.6) (18.2) 12.9
Accounts payable 2.6 65.5 (19.6)
Other (1.9) 23.5 9.0
Net cash provided by operating activities 316.3 408.7 504.8
Cash flows from investing activities:      
Purchases of property, plant, and equipment (56.5) (43.8) (54.9)
Proceeds from sale of property, plant, and equipment 8.9 4.7 0.2
Acquisitions of businesses, net of cash acquired (12.9) (75.3) (303.0)
Other investing activities (1.7) (3.5) (2.1)
Net cash used for investing activities (62.2) (117.9) (359.8)
Cash flows from financing activities:      
Borrowings on credit facility, net of repayments 18.0 0.0 0.0
Issuances of long-term debt 0.0 493.8 400.0
Repayments of long-term debt 0.0 (401.1) (355.7)
Repurchases of common stock (514.8) (434.9) (69.3)
Proceeds from stock option exercises and other 12.5 3.2 0.9
Payments of taxes withheld on net settlement of equity awards (8.6) (4.5) (5.4)
Dividends paid (18.1) (19.1) (20.8)
Other financing activities (1.4) 0.0 0.0
Net cash used for financing activities (512.4) (362.6) (50.3)
Effect of exchange rate changes on cash and cash equivalents (9.8) 2.4 5.0
Net change in cash and cash equivalents (268.1) (69.4) 99.7
Cash and cash equivalents at beginning of year 491.3 560.7 461.0
Cash and cash equivalents at end of year 223.2 491.3 560.7
Supplemental cash flow information:      
Income taxes paid 109.4 86.4 64.6
Interest paid $ 26.1 $ 22.2 $ 29.8