# Number of sequences of given type

Consider that there is sequence $$a$$ of length $$n$$ ,$$a=[a_i,0\le i\le n]$$. Now you are given with $$\text{lcm}$$ of some pairs of number from list that is, $$\operatorname{lcm}(a_i,a_j)=k$$ for $$0\le i,j\le n$$ and $$i\neq j$$ and $$k$$ is specific for given pair. Find number of sequences of $$a$$ that satisfy given $$\text{lcm}$$‘s.

I thought that if $$\text{lcm}$$ pairs are less than number of distinct number of pairs from sequence,than answer if infinity and if there is any contradicting pair then answer is $$0$$ and for remaining case that is where $$\text{lcm}$$ involving every element is present then i do not know how to solve. Could anyone help me with this question.