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DIVESTITURES - Summary of Components of Income from Discontinued Operations before Income Taxes (Details) - Discontinued Operations, Disposed of by Sale - HHI Segment - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]      
Net sales $ 1,652.3 $ 1,615.8 $ 1,342.1
Cost of goods sold 1,096.3 1,025.3 850.3
Gross profit 556.0 590.5 491.8
Operating expenses 298.0 293.1 257.1
Operating income 258.0 297.4 234.7
Interest expense 3.4 3.4 3.5
Other non-operating expense, net 1.3 5.8 3.4
Income from discontinued operations before income taxes $ 253.3 $ 288.2 $ 227.8