Goodwill and Intangible Assets (Schedule of Amortizable Intangible Assets) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Mar. 31, 2024	Mar. 31, 2023	Mar. 31, 2024	Mar. 31, 2023	Sep. 30, 2023
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	$ 690.2		$ 690.2		$ 688.8
Amortizable intangible assets, accumulated amortization	324.4		324.4		307.9
Amortizable intangible assets, net	365.8		365.8		380.9
Other intangible assets, net	960.4		960.4		973.8
Intangible Assets, Gross (Excluding Goodwill)	1,284.8		1,284.8		1,281.7
Amortization of intangibles	7.8	$ 7.7	15.6	$ 15.4
Amortizable intangible assets, amortization expense, remainder of 2023	15.5		15.5
Amortizable intangible assets, amortization expense, fiscal 2024	31.1		31.1
Amortizable intangible assets, amortization expense, fiscal 2025	30.7		30.7
Amortizable intangible assets, amortization expense, fiscal 2026	30.5		30.5
Amortizable intangible assets, amortization expense, fiscal 2027	30.4		30.4
Amortizable intangible assets, amortization expense, fiscal 2028	30.4		30.4
Amortizable intangible assets, amortization expense, after fiscal 2028	197.2		197.2
Indefinite-lived intangible assets	594.6		594.6		592.9
Trade names and brands
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	339.6		339.6		339.6
Amortizable intangible assets, accumulated amortization	96.1		96.1		88.1
Amortizable intangible assets, net	243.5		243.5		251.5
Technology and patents
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	79.6		79.6		79.4
Amortizable intangible assets, accumulated amortization	76.7		76.7		76.2
Amortizable intangible assets, net	2.9		2.9		3.2
Customer related and other
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	271.0		271.0		269.8
Amortizable intangible assets, accumulated amortization	151.6		151.6		143.6
Amortizable intangible assets, net	$ 119.4		$ 119.4		$ 126.2