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Goodwill and Intangible Assets - Changes in Goodwill (Details) - USD ($)
$ in Millions
3 Months Ended
Nov. 30, 2022
Nov. 30, 2021
Goodwill [Roll Forward]    
Goodwill, Beginning Balance $ 1,084.3 $ 1,094.7
Derecognitions for divestitures (0.7)  
Foreign currency translation adjustments (1.6) (3.7)
Goodwill, Ending Balance 1,082.0 1,091.0
ABL    
Goodwill [Roll Forward]    
Goodwill, Beginning Balance 1,014.2 1,022.2
Derecognitions for divestitures (0.7)  
Foreign currency translation adjustments (0.4) (3.0)
Goodwill, Ending Balance 1,013.1 1,019.2
ISG    
Goodwill [Roll Forward]    
Goodwill, Beginning Balance 70.1 72.5
Derecognitions for divestitures 0.0  
Foreign currency translation adjustments (1.2) (0.7)
Goodwill, Ending Balance $ 68.9 $ 71.8