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Revenue Recognition - Disaggregated Revenues (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Feb. 28, 2023	Feb. 28, 2022	Feb. 28, 2023	Feb. 28, 2022
Disaggregation of Revenue [Line Items]
Total sales	$ 943.6	$ 909.1	$ 1,941.5	$ 1,835.2
Operating Segments | ABL
Disaggregation of Revenue [Line Items]
Total sales	890.8	863.1	1,837.9	1,746.7
Operating Segments | ISG
Disaggregation of Revenue [Line Items]
Total sales	58.2	50.0	115.0	96.4
Eliminations
Disaggregation of Revenue [Line Items]
Total sales	(5.4)	(4.0)	(11.4)	(7.9)
Independent sales network | Operating Segments | ABL
Disaggregation of Revenue [Line Items]
Total sales	635.3	614.3	1,309.0	1,251.1
Direct sales network | Operating Segments | ABL
Disaggregation of Revenue [Line Items]
Total sales	94.7	83.2	201.1	173.2
Retail sales | Operating Segments | ABL
Disaggregation of Revenue [Line Items]
Total sales	50.4	42.7	100.3	89.6
Corporate accounts | Operating Segments | ABL
Disaggregation of Revenue [Line Items]
Total sales	54.0	53.6	103.1	90.6
OEM and other | Operating Segments | ABL
Disaggregation of Revenue [Line Items]
Total sales	$ 56.4	$ 69.3	$ 124.4	$ 142.2

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