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Acquisitions - Narrative (Details) $ in Millions | 3 Months Ended |  |  |
--- | --- | --- | --- | ---
Nov. 30, 2020 USD ($) brand acquisition | Aug. 31, 2020 USD ($) | Nov. 30, 2019 USD ($) | Aug. 31, 2019 USD ($)
Business Acquisition [Line Items] |  |  |  |
Number of acquisitions completed | acquisition | 0 |  |  |
Goodwill | $ 1,080.6 | $ 1,080.0 | $ 1,115.5 | $ 967.3
The Luminaires Group (TLG) |  |  |  |
Business Acquisition [Line Items] |  |  |  |
Number of niche lighting brands | brand | 5 |  |  |
Fiscal 2020 Acquisitions |  |  |  |
Business Acquisition [Line Items] |  |  |  |
Goodwill | $ 107.6 |  |  |
Identified intangible assets | $ 180.6 |  |  |
Weighted average useful life of acquired intangible assets | 16 years |  |  |
Goodwill expected to be tax deductible | $ 77.7 |  |  |

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