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Segment Information (Details)
$ in Millions
12 Months Ended
Aug. 31, 2025
USD ($)
segment
Aug. 31, 2024
USD ($)
Aug. 31, 2023
USD ($)
Segment Reporting [Abstract]      
Number of reportable segments | segment 2    
Geographic Distribution      
Net sales $ 4,345.6 $ 3,841.0 $ 3,952.2
Cost of goods sold 2,267.1 2,059.3 2,239.0
Selling, distribution, and administrative expenses 1,484.9 1,228.4 1,212.9
Special charges 29.7 0.0 26.9
Operating profit 563.9 553.3 473.4
Interest expense, net 22.0 (4.5) 18.9
Miscellaneous expense, net 41.7 9.2 7.8
Income before income taxes 500.2 548.6 446.7
Supplemental Information:      
Depreciation and amortization 133.1 91.1 93.2
Segment assets 4,755.2 3,814.6 3,408.5
Capital expenditures 68.4 64.0 66.7
Operating Segments | ABL      
Geographic Distribution      
Net sales 3,612.2 3,573.4 3,722.8
Cost of goods sold 1,957.7 1,960.9 2,152.5
Selling, distribution, and administrative expenses 1,034.2 1,029.7 1,035.8
Special charges 29.7   25.0
Operating profit 590.6 582.8 509.5
Supplemental Information:      
Depreciation and amortization 71.0 74.7 77.4
Segment assets 906.1 883.9 870.4
Capital expenditures 55.1 55.1 60.2
Operating Segments | AIS      
Geographic Distribution      
Net sales 764.3 291.9 252.7
Cost of goods sold 340.3 122.7 109.8
Selling, distribution, and administrative expenses 347.9 125.6 110.8
Special charges 0.0   0.0
Operating profit 76.1 43.6 32.1
Supplemental Information:      
Depreciation and amortization 59.7 15.3 14.4
Segment assets 214.5 67.6 53.7
Capital expenditures 10.4 3.6 3.5
Corporate      
Geographic Distribution      
Net sales 0.0 0.0 0.0
Cost of goods sold 0.0 0.0 0.0
Selling, distribution, and administrative expenses 102.8 73.1 66.3
Special charges 0.0   1.9
Operating profit (102.8) (73.1) (68.2)
Supplemental Information:      
Depreciation and amortization 2.4 1.1 1.4
Segment assets 3,634.6 2,863.1 2,484.4
Capital expenditures 2.9 5.3 3.0
Eliminations      
Geographic Distribution      
Net sales (30.9) (24.3) (23.3)
Cost of goods sold (30.9) (24.3) (23.3)
Selling, distribution, and administrative expenses 0.0 0.0 0.0
Special charges 0.0   0.0
Operating profit 0.0 0.0 0.0
Supplemental Information:      
Depreciation and amortization 0.0 0.0 0.0
Segment assets 0.0 0.0 0.0
Capital expenditures $ 0.0 $ 0.0 $ 0.0