Segment Information - Segments Internal Financial Reports (Detail) - USD ($) $ in Millions	12 Months Ended
	Aug. 31, 2023	Aug. 31, 2022	Aug. 31, 2021
Segment Reporting Information [Line Items]
Revenue	$ 3,944.0	$ 2,977.7	$ 1,747.9
Earnings (loss) from operations	176.4	118.0	41.0
Assets	3,978.4	3,851.5	3,390.7
Depreciation and amortization	106.3	102.0	100.7
Capital expenditures	362.1	380.7	139.0
Manufacturing
Segment Reporting Information [Line Items]
Revenue	3,357.7	2,476.6	1,311.1
Maintenance Services
Segment Reporting Information [Line Items]
Revenue	406.4	347.7	298.3
Leasing & Management Services
Segment Reporting Information [Line Items]
Revenue	179.9	153.4	138.5
Corporate, Non-Segment
Segment Reporting Information [Line Items]
Earnings (loss) from operations	(104.7)	(109.2)	(82.7)
Intersegment Eliminations
Segment Reporting Information [Line Items]
Revenue	(344.3)	(219.9)	(102.6)
Earnings (loss) from operations	(29.0)	(12.0)	(7.2)
Intersegment Eliminations | Manufacturing
Segment Reporting Information [Line Items]
Revenue	307.1	191.6	92.4
Earnings (loss) from operations	28.7	11.9	6.9
Intersegment Eliminations | Maintenance Services
Segment Reporting Information [Line Items]
Revenue	36.0	26.4	9.1
Earnings (loss) from operations			0.1
Intersegment Eliminations | Leasing & Management Services
Segment Reporting Information [Line Items]
Revenue	1.2	1.9	1.1
Earnings (loss) from operations	0.3	0.1	0.2
Operating Segments | Manufacturing
Segment Reporting Information [Line Items]
Revenue	3,664.8	2,668.2	1,403.5
Earnings (loss) from operations	169.6	109.1	55.2
Assets	1,847.0	1,853.9	1,493.5
Depreciation and amortization	60.3	61.7	67.8
Capital expenditures	71.9	48.3	26.6
Operating Segments | Maintenance Services
Segment Reporting Information [Line Items]
Revenue	442.4	374.1	307.4
Earnings (loss) from operations	36.9	21.7	6.6
Assets	294.4	284.8	260.9
Depreciation and amortization	10.5	10.7	12.0
Capital expenditures	17.3	9.2	8.6
Operating Segments | Leasing & Management Services
Segment Reporting Information [Line Items]
Revenue	181.1	155.3	139.6
Earnings (loss) from operations	103.6	108.4	69.1
Assets	1,458.1	1,152.2	949.4
Depreciation and amortization	35.5	29.6	20.9
Capital expenditures	272.9	323.2	103.8
Operating Segments | Unallocated, including cash
Segment Reporting Information [Line Items]
Assets	378.9	560.6	686.9
Reconciling Items | Manufacturing
Segment Reporting Information [Line Items]
Earnings (loss) from operations	140.9	97.2	48.3
Reconciling Items | Maintenance Services
Segment Reporting Information [Line Items]
Earnings (loss) from operations	36.9	21.7	6.5
Reconciling Items | Leasing & Management Services
Segment Reporting Information [Line Items]
Earnings (loss) from operations	$ 103.3	$ 108.3	$ 68.9