... I am interested to know what the dpi is set to for cameras. For example when I open up a photo from my lumix it has 180 dpi.
So that means my image size has to go down if I want it at 300 dpi
If the canon image was was 5184x3456 at 180 dpi that would mean I would have to reduce image size to get dpi up.
1. Let's just start with a simple fact: the only thing that is set
for cameras is the file dimension in pixels, or, in your case, 5184x3456. Everything else is a calculated value based on that, like dpi. You can not say that a particular dpi is "set" for cameras, just as you can not say that a particular miles per hour (say 55mph) is set for cars. You can not thus say that your Lumix "has" 180 dpi.
To calculate dpi, you need two other elements: file size in pixels and print size in inches. Like in any math formula, when you have two elements, you can always calculate the third.
I suspect that, when you open your Lumix file and it "has" 180 dpi, you actually had previously set that value in software preferences (or the software manufacturer already set it for your convenience). It is an arbitrary number, and can be any other (like 72, 96, 240, 300 etc.) just as well. It is, however, a reasonably well chosen number, as it corresponds with a minimum dpi necessary for high quality printing on glossy media. The reason a number like this exists in the Resolution field in Document/Image Size is to give you a starting point and an idea how big you can print with a reasonable quality. In absence of any number in the Resolution field, the other two fields (Width and Height) would also be empty.
2. If the Resolution field says "180," and you want to go to 300 dpi, your image size
is NOT going to go down (it will always remain the same, as 5184x3456). What is going to go down is your print size.
So, to answer your OP question, if you want to print to approximately 11.7" x 16.5" and you want it to be at 300 dpi, your camera should be able to deliver the file with 4950 x 3510 px. So, a camera with 5184 x 3456 px would be sufficient.