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Goodwill and Purchased Intangible Assets - Schedule of Purchased Intangible Assets (Details) - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Acquired Finite Lived Intangible Assets [Line Items]    
Weighted- Average Life (in years) 14 years 4 months 24 days 14 years 8 months 12 days
Gross $ 756.3 $ 731.2
Accumulated Amortization (706.6) (697.7)
Net 49.7 33.5
Non-amortizable trade names 417.1 384.7
Intangible assets excluding goodwill, gross 1,173.4 1,115.9
Purchased intangible assets, net $ 466.8 $ 418.2
Distribution network    
Acquired Finite Lived Intangible Assets [Line Items]    
Weighted- Average Life (in years) 39 years 1 month 6 days 39 years 1 month 6 days
Gross $ 55.4 $ 55.4
Accumulated Amortization (35.1) (33.8)
Net $ 20.3 $ 21.6
Technology-related    
Acquired Finite Lived Intangible Assets [Line Items]    
Weighted- Average Life (in years) 11 years 10 months 24 days 11 years 10 months 24 days
Gross $ 104.7 $ 104.7
Accumulated Amortization (103.9) (103.3)
Net $ 0.8 $ 1.4
Customer relationships    
Acquired Finite Lived Intangible Assets [Line Items]    
Weighted- Average Life (in years) 12 years 7 months 6 days 12 years 9 months 18 days
Gross $ 572.6 $ 554.7
Accumulated Amortization (550.0) (545.6)
Net $ 22.6 $ 9.1
Other    
Acquired Finite Lived Intangible Assets [Line Items]    
Weighted- Average Life (in years) 12 years 1 month 6 days 16 years 3 months 18 days
Gross $ 23.6 $ 16.4
Accumulated Amortization (17.6) (15.0)
Net $ 6.0 $ 1.4