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Segment Information - Segments Internal Financial Reports (Detail) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Feb. 28, 2025	Feb. 29, 2024	Feb. 28, 2025	Feb. 29, 2024	Aug. 31, 2024
Segment Reporting Information [Line Items]
Revenue	$ 762.1	$ 862.7	$ 1,638.0	$ 1,671.5
Earnings (loss) from operations	83.6	63.5	195.4	128.4
Assets	4,267.0		4,267.0		$ 4,254.5
Manufacturing
Segment Reporting Information [Line Items]
Revenue	700.3	811.0	1,520.7	1,570.7
Leasing & Fleet Management
Segment Reporting Information [Line Items]
Revenue	61.8	51.7	117.3	100.8
Corporate, Non-Segment
Segment Reporting Information [Line Items]
Revenue
Earnings (loss) from operations	(31.0)	(33.1)	(62.0)	(59.4)
Intersegment Eliminations
Segment Reporting Information [Line Items]
Revenue	(53.3)	(63.4)	(56.3)	(122.3)
Earnings (loss) from operations	(9.7)	(3.8)	(9.7)	(8.5)
Intersegment Eliminations | Manufacturing
Segment Reporting Information [Line Items]
Revenue	53.1	63.1	55.9	121.8
Earnings (loss) from operations	9.7	3.7	9.7	8.4
Intersegment Eliminations | Leasing & Fleet Management
Segment Reporting Information [Line Items]
Revenue	0.2	0.3	0.4	0.5
Earnings (loss) from operations		0.1		0.1
Operating Segments | Manufacturing
Segment Reporting Information [Line Items]
Revenue	753.4	874.1	1,576.6	1,692.5
Earnings (loss) from operations	78.7	67.1	194.8	136.7
Assets	2,042.0		2,042.0		2,172.4
Operating Segments | Leasing & Fleet Management
Segment Reporting Information [Line Items]
Revenue	62.0	52.0	117.7	101.3
Earnings (loss) from operations	45.6	33.3	72.3	59.6
Assets	1,854.9		1,854.9		1,633.6
Operating Segments | Unallocated, including cash
Segment Reporting Information [Line Items]
Assets	370.1		370.1		$ 448.5
Reconciling Items | Manufacturing
Segment Reporting Information [Line Items]
Earnings (loss) from operations	69.0	63.4	185.1	128.3
Reconciling Items | Leasing & Fleet Management
Segment Reporting Information [Line Items]
Earnings (loss) from operations	$ 45.6	$ 33.2	$ 72.3	$ 59.5

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