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Goodwill and Intangible Assets - Schedule of Changes in Goodwill (Details) - USD ($)
$ in Millions
 6 Months Ended
Feb. 29, 2024
Feb. 28, 2023
Goodwill [Roll Forward]    
Goodwill, beginning balance $ 1,097.9 $ 1,084.3
Derecognitions for divestitures   (0.7)
Foreign currency translation adjustments (0.8) (3.3)
Goodwill, ending balance 1,097.1 1,080.3
ABL    
Goodwill [Roll Forward]    
Goodwill, beginning balance 1,014.4 1,014.2
Derecognitions for divestitures   (0.7)
Foreign currency translation adjustments (0.6) (1.2)
Goodwill, ending balance 1,013.8 1,012.3
ISG    
Goodwill [Roll Forward]    
Goodwill, beginning balance 83.5 70.1
Derecognitions for divestitures   0.0
Foreign currency translation adjustments (0.2) (2.1)
Goodwill, ending balance $ 83.3 $ 68.0