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I have software licensed under LGPL 2.1 and I want to modify it and re-publish the whole software under the GPL 3.0 license. Is this legally possible?

I think so, but I'm not completely sure.

LGPL 2.1 says

...3. You may opt to apply the terms of the ordinary GNU General Public License instead of this License to a given copy of the Library. To do this, you must alter all the notices that refer to this License, so that they refer to the ordinary GNU General Public License, version 2, instead of to this License. (If a newer version than version 2 of the ordinary GNU General Public License has appeared, then you can specify that version instead if you wish.) Do not make any other change in these notices. ...

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You have interpreted the license correctly. A LGPL v2.1 covered work can be relicensed under GPL v2+, which includes the GPL v3.

The GPL license compatibility matrix in the GPL FAQ confirms this and explains:

LGPLv2.1 gives you permission to relicense the code under any version of the GPL since GPLv2.

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  • Thanks. I remember to have seen the license compatibility matrix at some point in the past but couldn't find it yesterday.
    – Trilarion
    May 23, 2018 at 12:05

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