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Supplemental Disaggregated Information (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 31, 2023	Aug. 31, 2022	Aug. 31, 2021
Geographic Distribution
Net sales	$ 3,952.2	$ 4,006.1	$ 3,461.0
Operating profit:	473.4	509.7	427.6
Income before income taxes:	446.7	493.9	396.2
Long-lived assets	431.2	399.4	361.0
Domestic
Geographic Distribution
Net sales	3,412.9	3,486.4	2,982.4
Operating profit:	382.6	428.3	369.9
Income before income taxes:	367.5	409.6	343.7
Long-lived assets	323.8	325.9	284.4
International
Geographic Distribution
Net sales	539.3	519.7	478.6
Operating profit:	90.8	81.4	57.7
Income before income taxes:	79.2	84.3	52.5
Long-lived assets	$ 107.4	$ 73.5	$ 76.6
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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