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Goodwill and Intangible Assets - Schedule of Changes in Goodwill (Details) - USD ($)
$ in Millions
 9 Months Ended
May 31, 2024
May 31, 2023
Goodwill [Roll Forward]    
Goodwill, beginning balance $ 1,097.9 $ 1,084.3
Provisional amounts from acquired businesses   15.2
Derecognitions for divestitures   (0.7)
Foreign currency translation adjustments (1.2) (2.1)
Goodwill, ending balance 1,096.7 1,096.7
ABL    
Goodwill [Roll Forward]    
Goodwill, beginning balance 1,014.4 1,014.2
Provisional amounts from acquired businesses   0.0
Derecognitions for divestitures   (0.7)
Foreign currency translation adjustments (0.7) (0.2)
Goodwill, ending balance 1,013.7 1,013.3
ISG    
Goodwill [Roll Forward]    
Goodwill, beginning balance 83.5 70.1
Provisional amounts from acquired businesses   15.2
Derecognitions for divestitures   0.0
Foreign currency translation adjustments (0.5) (1.9)
Goodwill, ending balance $ 83.0 $ 83.4