The DNA molecule is primarily found in the nucleus of a living cell. This is where the majority of the cell's DNA is stored and organized into chromosomes.

However, there are some exceptions:

* Mitochondria: These organelles have their own DNA, separate from the nuclear DNA. This is known as mitochondrial DNA (mtDNA).

* Chloroplasts: In plant cells, these organelles also contain their own DNA, called chloroplast DNA (cpDNA).

So, while the nucleus is the main location for DNA, a small amount can also be found in mitochondria and chloroplasts.