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Segment Information - Operating Segment (Details)
$ in Millions
 3 Months Ended 12 Months Ended
May 31, 2021
reporting_unit
Aug. 31, 2021
USD ($)
statement
Aug. 31, 2020
USD ($)
Aug. 31, 2019
USD ($)
Segment Reporting [Abstract]        
Number of reportable segments 2 2    
Segment Reporting Information [Line Items]        
Net sales   $ 3,461.0 $ 3,326.3 $ 3,672.7
Operating profit (loss)   427.6 353.9 462.9
Depreciation and amortization   100.1 101.1 88.3
Operating Segments | ABL        
Segment Reporting Information [Line Items]        
Net sales   3,287.3 3,180.9 3,548.4
Operating profit (loss)   476.2 425.8 510.2
Depreciation and amortization   84.3 83.7 72.6
Operating Segments | ISG        
Segment Reporting Information [Line Items]        
Net sales   190.0 157.0 137.5
Operating profit (loss)   9.9 (3.9) (18.1)
Depreciation and amortization   14.7 16.3 14.6
Corporate        
Segment Reporting Information [Line Items]        
Net sales   0.0 0.0 0.0
Operating profit (loss)   (58.5) (68.0) (29.2)
Depreciation and amortization   1.1 1.1 1.1
Eliminations        
Segment Reporting Information [Line Items]        
Net sales   (16.3) (11.6) (13.2)
Operating profit (loss)   0.0 0.0 0.0
Depreciation and amortization   $ 0.0 $ 0.0 $ 0.0