Goodwill and Intangible Assets (Schedule of Amortizable Intangible Assets) (Details) - USD ($) $ in Millions	3 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Sep. 30, 2021
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	$ 692.3		$ 556.5
Amortizable intangible assets, accumulated amortization	256.7		250.9
Amortizable intangible assets, net	435.6		305.6
Amortization of intangibles	6.1	$ 5.5
Amortizable intangible assets, amortization expense, remainder of 2022	23.2
Amortizable intangible assets, amortization expense, fiscal 2023	30.9
Amortizable intangible assets, amortization expense, fiscal 2024	30.8
Amortizable intangible assets, amortization expense, fiscal 2025	30.8
Amortizable intangible assets, amortization expense, fiscal 2026	30.6
Amortizable intangible assets, amortization expense, fiscal 2027	30.5
Amortizable intangible assets, amortization expense, after fiscal 2027	258.8
Indefinite-lived Intangible Assets [Line Items]
Indefinite-lived intangible assets	599.4		600.8
Trade names and brands
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	339.9		256.2
Amortizable intangible assets, accumulated amortization	61.1		57.7
Amortizable intangible assets, net	278.8		198.5
Technology and patents
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	78.9		79.1
Amortizable intangible assets, accumulated amortization	75.7		75.8
Amortizable intangible assets, net	3.2		3.3
Customer related and other
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	273.5		221.2
Amortizable intangible assets, accumulated amortization	119.9		117.4
Amortizable intangible assets, net	$ 153.6		$ 103.8