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Supplemental Disaggregated Information (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 31, 2022	Aug. 31, 2021	Aug. 31, 2020
Geographic Distribution
Net sales	$ 4,006.1	$ 3,461.0	$ 3,326.3
Operating profit:	509.7	427.6	353.9
Income before income taxes:	493.9	396.2	324.7
Long-lived assets	399.4	361.0	363.4
Domestic
Geographic Distribution
Net sales	3,486.4	2,982.4	2,925.0
Operating profit:	428.3	369.9	300.6
Income before income taxes:	409.6	343.7	274.2
Long-lived assets	325.9	284.4	298.6
International
Geographic Distribution
Net sales	519.7	478.6	401.3
Operating profit:	81.4	57.7	53.3
Income before income taxes:	84.3	52.5	50.5
Long-lived assets	$ 73.5	$ 76.6	$ 64.8
Net Sales | Product Concentration Risk | Lighting and Building Management Solutions
Geographic Distribution
Concentrations as a percentage of total (percent)	99.00%	99.00%	99.00%

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