Income Taxes - Schedule of Components of Net Deferred Income Taxes (Details) - USD ($) $ in Millions	Aug. 31, 2024	Aug. 31, 2023
Deferred income tax liabilities:
Depreciation	$ (21.8)	$ (21.5)
Goodwill and intangibles	(150.2)	(151.2)
Operating lease right of use assets	(15.8)	(19.8)
Other liabilities	(1.8)	(3.4)
Total deferred income tax liabilities	(189.6)	(195.9)
Deferred income tax assets:
Self-insurance	2.1	1.7
Pension	6.7	5.9
Deferred compensation	24.5	23.1
Net operating losses	7.1	6.2
Other accruals not yet deductible	43.3	43.4
Operating lease liabilities	18.5	22.6
Capitalized research and development	70.1	41.5
Other assets	14.0	15.4
Total deferred income tax assets	186.3	159.8
Valuation allowance	(20.4)	(19.9)
Net deferred income tax liabilities	$ (23.7)	$ (56.0)