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Segment Information (Details)
$ in Millions
 3 Months Ended 9 Months Ended
May 31, 2021
USD ($)
Segment
May 31, 2020
USD ($)
May 31, 2021
USD ($)
May 31, 2020
USD ($)
Segment Reporting [Abstract]        
Number of reportable segments | Segment 2      
Segment Reporting Information [Line Items]        
Net sales $ 899.7 $ 776.2 $ 2,468.3 $ 2,435.1
Operating profit (loss) 118.1 83.0 294.8 248.0
Depreciation and amortization 25.0 25.5 75.0 75.3
Interest expense, net 6.2 5.4 17.7 19.4
Miscellaneous expense (income), net 2.7 (0.9) 6.5 1.5
Income before income taxes 109.2 78.5 270.6 227.1
Operating segments | ABL        
Segment Reporting Information [Line Items]        
Net sales 850.0 741.6 2,340.4 2,327.8
Operating profit (loss) 126.5 98.6 326.9 304.0
Depreciation and amortization 21.0 20.8 63.2 62.5
Operating segments | ISG        
Segment Reporting Information [Line Items]        
Net sales 55.4 37.7 139.5 116.1
Operating profit (loss) 7.2 (0.2) 7.9 (2.3)
Depreciation and amortization 3.7 4.4 11.0 12.0
Corporate        
Segment Reporting Information [Line Items]        
Net sales 0.0 0.0 0.0 0.0
Operating profit (loss) (15.6) (15.4) (40.0) (53.7)
Depreciation and amortization 0.3 0.3 0.8 0.8
Eliminations        
Segment Reporting Information [Line Items]        
Net sales (5.7) (3.1) (11.6) (8.8)
Operating profit (loss) 0.0 0.0 0.0 0.0
Depreciation and amortization $ 0.0 $ 0.0 $ 0.0 $ 0.0