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Segment Information - Segments Internal Financial Reports (Detail) - USD ($)
$ in Millions
 12 Months Ended
Aug. 31, 2024
Aug. 31, 2023
Aug. 31, 2022
Segment Reporting Information [Line Items]      
Revenue $ 3,544.7 $ 3,944.0 $ 2,977.7
Earnings (loss) from operations 324.5 176.4 118.0
Assets 4,254.5 3,978.4 3,851.5
Depreciation and amortization 115.6 106.3 102.0
Capital expenditures 398.3 362.1 380.7
Manufacturing      
Segment Reporting Information [Line Items]      
Revenue 3,013.6 3,357.7 2,476.6
Maintenance Services      
Segment Reporting Information [Line Items]      
Revenue 298.8 406.4 347.7
Leasing & Management Services      
Segment Reporting Information [Line Items]      
Revenue 232.3 179.9 153.4
Corporate, Non-Segment      
Segment Reporting Information [Line Items]      
Earnings (loss) from operations (123.2) (104.7) (109.2)
Intersegment Eliminations      
Segment Reporting Information [Line Items]      
Revenue (279.5) (344.3) (219.9)
Earnings (loss) from operations (25.0) (29.0) (12.0)
Intersegment Eliminations | Manufacturing      
Segment Reporting Information [Line Items]      
Revenue 228.8 307.1 191.6
Earnings (loss) from operations 24.9 28.7 11.9
Intersegment Eliminations | Maintenance Services      
Segment Reporting Information [Line Items]      
Revenue 49.7 36.0 26.4
Earnings (loss) from operations     0.0
Intersegment Eliminations | Leasing & Management Services      
Segment Reporting Information [Line Items]      
Revenue 1.0 1.2 1.9
Earnings (loss) from operations 0.1 0.3 0.1
Operating Segments | Manufacturing      
Segment Reporting Information [Line Items]      
Revenue 3,242.4 3,664.8 2,668.2
Earnings (loss) from operations 306.5 169.6 109.1
Assets 1,881.2 1,847.0 1,853.9
Depreciation and amortization 102.8 71.9 48.3
Capital expenditures 61.5 60.3 61.7
Operating Segments | Maintenance Services      
Segment Reporting Information [Line Items]      
Revenue 348.5 442.4 374.1
Earnings (loss) from operations 27.1 36.9 21.7
Assets 18.5 17.3 9.2
Depreciation and amortization 10.6 10.5 10.7
Capital expenditures 291.2 294.4 284.8
Operating Segments | Leasing & Management Services      
Segment Reporting Information [Line Items]      
Revenue 233.3 181.1 155.3
Earnings (loss) from operations 139.1 103.6 108.4
Assets 1,633.6 1,458.1 1,152.2
Depreciation and amortization 277.0 272.9 323.2
Capital expenditures 43.5 35.5 29.6
Operating Segments | Unallocated, including cash      
Segment Reporting Information [Line Items]      
Assets 448.5 378.9 560.6
Reconciling Items | Manufacturing      
Segment Reporting Information [Line Items]      
Earnings (loss) from operations 281.6 140.9 97.2
Reconciling Items | Maintenance Services      
Segment Reporting Information [Line Items]      
Earnings (loss) from operations 27.1 36.9 21.7
Reconciling Items | Leasing & Management Services      
Segment Reporting Information [Line Items]      
Earnings (loss) from operations $ 139.0 $ 103.3 $ 108.3