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Goodwill and Intangible Assets (Tables) | 6 Months Ended
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Feb. 28, 2023
Goodwill and Intangible Assets Disclosure [Abstract] |
Schedule of Future Amortization Expense | The following table summarizes the expected amortization expense for the next five fiscal years as of the date presented (in millions):
Fiscal Year |  | February 28, 2023
2023 |  | $ | 41.5 |
2024 |  | 36.9 |
2025 |  | 29.4 |
2026 |  | 26.7 |
2027 |  | 25.2 |
Schedule of Goodwill | The following table summarizes the changes in the carrying amount of goodwill by segment during the periods presented (in millions):
| ABL |  | ISG |  | Total
Balance as of August 31, 2022 | $ | 1,014.2 |  |  | $ | 70.1 |  |  | $ | 1,084.3 |
Derecognitions for divestitures | (0.7) |  |  | — |  |  | (0.7) |
Foreign currency translation adjustments | (1.2) |  |  | (2.1) |  |  | (3.3) |
Balance as of February 28, 2023 | $ | 1,012.3 |  |  | $ | 68.0 |  |  | $ | 1,080.3 |
| ABL |  | ISG |  | Total
Balance as of August 31, 2021 | $ | 1,022.2 |  |  | $ | 72.5 |  |  | $ | 1,094.7 |
Adjustments to provisional amounts from acquired businesses | 0.6 |  |  | — |  |  | 0.6 |
Foreign currency translation adjustments | (2.6) |  |  | (0.3) |  |  | (2.9) |
Balance as of February 28, 2022 | $ | 1,020.2 |  |  | $ | 72.2 |  |  | $ | 1,092.4 |

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