Property, Plant, and Equipment - Schedule of Property, Plant, and Equipment (Details) - USD ($) $ in Millions |
Feb. 29, 2024 |
Aug. 31, 2023 |
|---|---|---|
| Property, Plant and Equipment [Line Items] | ||
| Total property, plant, and equipment, at cost | $ 981.2 | $ 961.8 |
| Less: Accumulated depreciation and amortization | (685.2) | (664.2) |
| Property, plant, and equipment, net | 296.0 | 297.6 |
| Land | ||
| Property, Plant and Equipment [Line Items] | ||
| Total property, plant, and equipment, at cost | 23.0 | 23.0 |
| Buildings and leasehold improvements | ||
| Property, Plant and Equipment [Line Items] | ||
| Total property, plant, and equipment, at cost | 214.7 | 210.9 |
| Machinery and equipment | ||
| Property, Plant and Equipment [Line Items] | ||
| Total property, plant, and equipment, at cost | $ 743.5 | $ 727.9 |