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Segment Reporting - Income Before Income Taxes (Details) - USD ($)
$ in Millions
3 Months Ended 12 Months Ended
Aug. 31, 2023
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Geographic Distribution        
Operating profit:   $ 473.4 $ 509.7 $ 427.6
Interest expense, net   18.9 24.9 23.2
Miscellaneous expense (income), net   7.8 (9.1) 8.2
Income before income taxes   446.7 493.9 396.2
Trade name impairment charges   14.0   0.0
Employee severance costs   7.7   1.7
ABL        
Geographic Distribution        
Employee severance costs $ 4.1      
Charge for collectability of a supplier warranty obligation 13.0      
ABL | Trade Names        
Geographic Distribution        
Trade name impairment charges $ 14.0      
Operating Segments | ABL        
Geographic Distribution        
Operating profit:   509.5 545.6 476.2
Operating Segments | ISG        
Geographic Distribution        
Operating profit:   32.1 22.7 9.9
Unallocated corporate amounts        
Geographic Distribution        
Operating profit:   $ (68.2) $ (58.6) $ (58.5)