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Segment Information (Details)
$ in Millions
 3 Months Ended 9 Months Ended
May 31, 2022
USD ($)
May 31, 2021
USD ($)
May 31, 2022
USD ($)
segment
May 31, 2021
USD ($)
Segment Reporting [Abstract]        
Number of reportable segments | segment     2  
Segment Reporting Information [Line Items]        
Net sales $ 1,060.6 $ 899.7 $ 2,895.8 $ 2,468.3
Operating profit (loss) 142.7 118.1 360.1 294.8
Depreciation and amortization 23.5 25.0 71.4 75.0
Interest expense, net 6.2 6.2 18.1 17.7
Miscellaneous (income) expense, net (1.5) 2.7 (3.1) 6.5
Income before income taxes 138.0 109.2 345.1 270.6
Operating segments | ABL        
Segment Reporting Information [Line Items]        
Net sales 1,008.4 850.0 2,755.1 2,340.4
Operating profit (loss) 149.6 126.5 394.2 326.9
Depreciation and amortization 19.6 21.0 59.8 63.2
Operating segments | ISG        
Segment Reporting Information [Line Items]        
Net sales 58.3 55.4 154.7 139.5
Operating profit (loss) 9.2 7.2 12.4 7.9
Depreciation and amortization 3.6 3.7 10.8 11.0
Corporate        
Segment Reporting Information [Line Items]        
Net sales 0.0 0.0 0.0 0.0
Operating profit (loss) (16.1) (15.6) (46.5) (40.0)
Depreciation and amortization 0.3 0.3 0.8 0.8
Eliminations        
Segment Reporting Information [Line Items]        
Net sales (6.1) (5.7) (14.0) (11.6)
Operating profit (loss) 0.0 0.0 0.0 0.0
Depreciation and amortization $ 0.0 $ 0.0 $ 0.0 $ 0.0