My current laptop has an i5-7200U processor, I wanted to swap it out with an i7-2620M. In theory would it work? Been looking for socket types but can't find any information. Thanks.
No, despite the fact the 7200u is a soldered socket the cpus are completely different architectures, pin counts, and are not supported by the same chipsets.
Even if you could that older 2620m would actually be a downgrade. While it may have a slightly higher clock the 7200u's newer architecture can process more data than the 2620m.
If you find the WHOLE board for a specific model of laptop on Ebay with the higher-clocked i7u variant, you can switch those out, but the performance difference for the cost it will probably run you probably isn't worth it.
There can be tons of issues with swapping out laptop chips, because they usually have OEM motherboards with only so many CPUs capable of running, let alone being supported. You have to do a lot of digging for answers to what supports what and things like that. Then you would have to actually find a way to get said processor, and who knows how much money it would take. It would be more trouble and/or money than it is worth.
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Which would be valid if you were able to swap those CPU's, but you can't.