Well, from what I know (or seen for that matter), the internal components are built there, but the overall outer structure are built in S. Korea and Mexico. It is done in order to cut down on production costs (electronic components are the most expensive to manufacture in an electronic device), increase trade between the countries, and cut down tensions between the countries (which isn't going as according to plan).
So, Yes and No, but LG probably tries to be very discrete in where its electronic components are made due to political pressures so probably little or no markings on their internal components regarding their origins. If you don't believe so, you can also tell by the price at which they sell at, which is lower than even that of GE'S appliances (which are built in china and designed in USA).
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The most manufatured goods in South Korea are Samsung and LG.
SAMSUNG , LG , HYUNDAI ...etc.
LG cell phones are produced in South Korea
South Korea's political structure is a mostly-democratic capitalism and North Korea's political structure is a communist dictatorship. South Korea has benefited from extensive industrialization and trade, including Europe and the US, which do not deal with North Korea. The two countries represent a number of traditionally competing or hostile ethnic groups.
North Korea is really secretive, while South Korea is very prosperous and holds many relations with other nations. North Korea is very much conscious about their military, that they forgot about children going to schools, and also, it is so hard for a South Korean to enter North Korea, while South Korea open-handedly welcomes anyone from North Korea into their country. These are just some reasons that South Korea is very much better than South Korea. There are a lot more.