Segment Information - Segments Internal Financial Reports (Detail) - USD ($) $ in Millions	3 Months Ended
	Nov. 30, 2024	Nov. 30, 2023	Aug. 31, 2024
Segment Reporting Information [Line Items]
Revenue	$ 875.9	$ 808.8
Earnings (loss) from operations	111.8	64.9
Assets	4,287.5		$ 4,254.5
Manufacturing
Segment Reporting Information [Line Items]
Revenue	820.4	759.7
Leasing & Fleet Management
Segment Reporting Information [Line Items]
Revenue	55.5	49.1
Corporate, Non-Segment
Segment Reporting Information [Line Items]
Earnings (loss) from operations	(31.0)	(26.3)
Intersegment Eliminations
Segment Reporting Information [Line Items]
Revenue	(3.0)	(58.9)
Earnings (loss) from operations	0.0	(4.7)
Intersegment Eliminations | Manufacturing
Segment Reporting Information [Line Items]
Revenue	2.8	58.7
Earnings (loss) from operations	0.0	4.7
Intersegment Eliminations | Leasing & Fleet Management
Segment Reporting Information [Line Items]
Revenue	0.2	0.2
Operating Segments | Manufacturing
Segment Reporting Information [Line Items]
Revenue	823.2	818.4
Earnings (loss) from operations	116.1	69.6
Assets	2,134.7		2,172.4
Operating Segments | Leasing & Fleet Management
Segment Reporting Information [Line Items]
Revenue	55.7	49.3
Earnings (loss) from operations	26.7	26.3
Assets	1,775.3		1,633.6
Operating Segments | Unallocated, including cash
Segment Reporting Information [Line Items]
Assets	377.5		$ 448.5
Reconciling Items | Manufacturing
Segment Reporting Information [Line Items]
Earnings (loss) from operations	116.1	64.9
Reconciling Items | Leasing & Fleet Management
Segment Reporting Information [Line Items]
Earnings (loss) from operations	$ 26.7	$ 26.3