The LS40A is actually a notebook computer, and generally notebook have their own custom-built motherboards, so you really can't purchase replacements except either directly from the manufacturer (in this case, LG), or buy one used and swap the parts.
However, am I correct in assuming you are looking for the model of the motherboard because you are re-installing drivers? If so, you can get all the supported drivers you need from here:
http://www.notebook-driver.com/lg/lg-notebook-ls40als50a-driver-and-software/Cheers,
- Vern.
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