So i did post the same question a couple of hours ago and it got downvoted(not sure why) and no answers so I deleted it and tried to do my research.
I have the following lattice: $L=\langle(1,2,3),(8,0,-2),(6,-5,5)\rangle$ in $\mathbb{Z^3}$ and I have to find a simpler generator of this lattice. My idea was to write it as a matrix and try to reduce it as much as possible in a reduced row echelon form kind of thing. When I use normal RREF on this matrix I do get the identity matrix, but on nearly all of the steps comes a multiplication with a fraction, which I don't think can be done since we are in $\mathbb{Z}$, and I could't think of any integers operations to do with it in order to simplify it. Does it mean that it can't get any simpler? Is there any other way?
Thanks in advance for the help