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Acquisitions - Narrative (Details) $ in Millions | 9 Months Ended |  |  |  |
--- | --- | --- | --- | --- | ---
May 31, 2020 USD ($) | Sep. 17, 2019 brand | Aug. 31, 2019 USD ($) | May 31, 2019 USD ($) | Aug. 31, 2018 USD ($)
Business Acquisition [Line Items] |  |  |  |  |
Goodwill | $ 1,086.4 |  | $ 967.3 | $ 964.1 | $ 970.6
The Luminaires Group (TLG) |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |
Number of niche lighting brands | brand |  | 5 |  |  |
Fiscal 2020 Acquisitions |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |
Goodwill | 127.5 |  |  |  |
Identified intangible assets | $ 180.7 |  |  |  |
Weighted average useful life of acquired intangible assets | 16 years |  |  |  |

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