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Segment Reporting - Schedule of Income Before Income Taxes (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
May 31, 2024
May 31, 2023
May 31, 2024
May 31, 2023
Segment Reporting Information [Line Items]        
Operating profit $ 145.3 $ 143.3 $ 396.3 $ 363.7
Interest (income) expense, net (1.8) 3.9 (1.0) 16.2
Miscellaneous (income) expense, net (0.5) 0.7 1.2 6.1
Income before income taxes 147.6 138.7 396.1 341.4
Operating Segments | ABL        
Segment Reporting Information [Line Items]        
Operating profit 151.5 150.0 421.3 391.7
Operating Segments | ISG        
Segment Reporting Information [Line Items]        
Operating profit 12.5 8.6 26.9 22.7
Unallocated corporate amounts        
Segment Reporting Information [Line Items]        
Operating profit $ (18.7) $ (15.3) $ (51.9) $ (50.7)