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Segment Information (Details)
$ in Millions
 3 Months Ended 9 Months Ended
May 31, 2023
USD ($)
Feb. 28, 2023
USD ($)
Nov. 30, 2022
USD ($)
May 31, 2022
USD ($)
May 31, 2023
USD ($)
segment
May 31, 2022
USD ($)
Segment Reporting Information [Line Items]            
Number of reportable segments | segment         2  
Special charges $ 0.0 $ 0.0 $ 6.9 $ 0.0 $ 6.9 $ 0.0
Net sales 1,000.3     1,060.6 2,941.8 2,895.8
Operating profit (loss) 143.3     142.7 363.7 360.1
Depreciation and amortization 21.9     23.5 70.4 71.4
Interest expense, net 3.9     6.2 16.2 18.1
Miscellaneous expense (income), net 0.7     (1.5) 6.1 (3.1)
Income before income taxes 138.7     138.0 341.4 345.1
ABL            
Segment Reporting Information [Line Items]            
Special charges         6.9  
Operating Segments | ABL            
Segment Reporting Information [Line Items]            
Net sales 940.7     1,008.4 2,778.6 2,755.1
Operating profit (loss) 150.0     149.6 391.7 394.2
Depreciation and amortization 18.1     19.6 58.9 59.8
Operating Segments | ISG            
Segment Reporting Information [Line Items]            
Net sales 65.8     58.3 180.8 154.7
Operating profit (loss) 8.6     9.2 22.7 12.4
Depreciation and amortization 3.5     3.6 10.5 10.8
Corporate            
Segment Reporting Information [Line Items]            
Net sales 0.0     0.0 0.0 0.0
Operating profit (loss) (15.3)     (16.1) (50.7) (46.5)
Depreciation and amortization 0.3     0.3 1.0 0.8
Eliminations            
Segment Reporting Information [Line Items]            
Net sales (6.2)     (6.1) (17.6) (14.0)
Operating profit (loss) 0.0     0.0 0.0 0.0
Depreciation and amortization $ 0.0     $ 0.0 $ 0.0 $ 0.0