Goodwill and Intangible Assets (Schedule of Amortizable Intangible Assets) (Details) - USD ($) $ in Millions	3 Months Ended
	Dec. 31, 2023	Dec. 31, 2022	Sep. 30, 2023
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	$ 690.9		$ 688.8
Amortizable intangible assets, accumulated amortization	317.2		307.9
Amortizable intangible assets, net	373.7		380.9
Other intangible assets, net	970.1		973.8
Intangible Assets, Gross (Excluding Goodwill)	1,287.3		1,281.7
Amortization of intangibles	7.8	$ 7.7
Amortizable intangible assets, amortization expense, remainder of 2023	23.3
Amortizable intangible assets, amortization expense, fiscal 2024	31.1
Amortizable intangible assets, amortization expense, fiscal 2025	30.7
Amortizable intangible assets, amortization expense, fiscal 2026	30.5
Amortizable intangible assets, amortization expense, fiscal 2027	30.4
Amortizable intangible assets, amortization expense, fiscal 2028	30.4
Amortizable intangible assets, amortization expense, after fiscal 2028	197.3
Indefinite-lived intangible assets	596.4		592.9
Trade names and brands
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	339.8		339.6
Amortizable intangible assets, accumulated amortization	92.2		88.1
Amortizable intangible assets, net	247.6		251.5
Technology and patents
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	79.7		79.4
Amortizable intangible assets, accumulated amortization	76.7		76.2
Amortizable intangible assets, net	3.0		3.2
Customer related and other
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	271.4		269.8
Amortizable intangible assets, accumulated amortization	148.3		143.6
Amortizable intangible assets, net	$ 123.1		$ 126.2