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Goodwill and Purchased Intangible Assets - Schedule of Purchased Intangible Assets (Details) - USD ($) $ in Millions	9 Months Ended	12 Months Ended
	Jun. 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	$ 756.4	$ 731.2
Accumulated Amortization	(703.8)	(697.7)
Net	52.6	33.5
Non-amortizable trade names	417.1	384.7
Intangible assets excluding goodwill, gross	1,173.5	1,115.9
Purchased intangible assets, net	$ 469.7	$ 418.2
Distribution network
Acquired Finite Lived Intangible Assets [Line Items]
Weighted- Average Life (in years)	39 years 2 months 12 days	39 years 1 month 6 days
Gross	$ 55.3	$ 55.4
Accumulated Amortization	(34.8)	(33.8)
Net	$ 20.5	$ 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	$ 104.8	$ 104.7
Accumulated Amortization	(103.8)	(103.3)
Net	$ 1.0	$ 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	$ 572.7	$ 554.7
Accumulated Amortization	(548.5)	(545.6)
Net	$ 24.2	$ 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	(16.7)	(15.0)
Net	$ 6.9	$ 1.4

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