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Goodwill and Intangible Assets - Changes in Goodwill (Details) - USD ($)
$ in Millions
 6 Months Ended
Feb. 28, 2023
Feb. 28, 2022
Goodwill [Roll Forward]    
Goodwill, beginning balance $ 1,084.3 $ 1,094.7
Derecognitions for divestitures (0.7)  
Adjustments to provisional amounts from acquired businesses   0.6
Foreign currency translation adjustments (3.3) (2.9)
Goodwill, ending balance 1,080.3 1,092.4
ABL    
Goodwill [Roll Forward]    
Goodwill, beginning balance 1,014.2 1,022.2
Derecognitions for divestitures (0.7)  
Adjustments to provisional amounts from acquired businesses   0.6
Foreign currency translation adjustments (1.2) (2.6)
Goodwill, ending balance 1,012.3 1,020.2
ISG    
Goodwill [Roll Forward]    
Goodwill, beginning balance 70.1 72.5
Derecognitions for divestitures 0.0  
Adjustments to provisional amounts from acquired businesses   0.0
Foreign currency translation adjustments (2.1) (0.3)
Goodwill, ending balance $ 68.0 $ 72.2