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Intangible Assets - Summary of Goodwill (Details) - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Goodwill [Roll Forward]    
Goodwill, beginning balance $ 548.2 $ 512.8
Acquisitions 29.0 39.1
Currency translation 0.8 (3.7)
Goodwill, ending balance $ 578.0 $ 548.2