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Segment Information - Operating Segment (Details)
$ in Millions
 12 Months Ended
Aug. 31, 2024
USD ($)
segment
Aug. 31, 2023
USD ($)
Aug. 31, 2022
USD ($)
Segment Reporting [Abstract]      
Number of reportable segments | segment 2    
Segment Reporting Information [Line Items]      
Special charges $ 0.0 $ 26.9 $ 0.0
Net sales 3,841.0 3,952.2 4,006.1
Operating profit (loss): 553.3 473.4 509.7
Depreciation and amortization: 91.1 93.2 94.8
Segment assets: 3,814.6 3,408.5 3,480.2
Capital expenditures: 64.0 66.7 56.5
Eliminations      
Segment Reporting Information [Line Items]      
Net sales (24.3) (23.3) (20.1)
Unallocated corporate amounts      
Segment Reporting Information [Line Items]      
Operating profit (loss): (73.1) (68.2) (58.6)
Depreciation and amortization: 1.1 1.4 1.1
Segment assets: 2,864.0 2,484.7 2,328.6
Capital expenditures: 5.3 3.9 2.2
ABL      
Segment Reporting Information [Line Items]      
Special charges   25.0  
ABL | Operating Segments      
Segment Reporting Information [Line Items]      
Net sales 3,573.4 3,722.8 3,810.1
Operating profit (loss): 582.8 509.5 545.6
Depreciation and amortization: 74.7 77.4 79.3
Segment assets: 883.0 870.1 1,097.8
Capital expenditures: 55.1 59.3 51.7
ISG | Operating Segments      
Segment Reporting Information [Line Items]      
Net sales 291.9 252.7 216.1
Operating profit (loss): 43.6 32.1 22.7
Depreciation and amortization: 15.3 14.4 14.4
Segment assets: 67.6 53.7 53.8
Capital expenditures: $ 3.6 $ 3.5 $ 2.6