The construction of binary Locally Repairable Code (LRC) achieving C-M (Cadambe-Mazumdar) bound has been fully studied while there are few researches on general fields. In order to solve the problem, the construction of LRC on general fields was studied. Firstly, a method for determining the number of elements in sunflower was proposed by projective geometry theory. Then, the parameters such as code length, dimension and locality of LRC were clearly described by depicting LRC through the disjoint repair group. Finally, based on the parity-check matrix with disjoint local repair group, two families of LRC on general fields with the minimum distance of 6 were constructed by sunflower, many of which were optimal or almost optimal. Compared with the existing LRC constructed by methods such as subfield subcode, generalized concatenated code and algebraic curve, the constructed two families of codes improve the information rate under the same code minimum distance and locality. These results can be applied to the construction of other LRC on general fields.