14. Given two non-decreasing sequences of non-negative integers, with different first terms, and each subsequent term in the sequences is the sum of the two preceding terms. If the seventh term of both sequences is $N$, then the smallest possible value of $N$ is $(\quad)$.
(A) 55
(B) 89
(C) 104
(D) 144
(E) 273
14. C.

Let the first two terms of the first sequence be $x_{1}, x_{2}\left(x_{1}, x_{2} \in \mathrm{N}\right)$, and the first two terms of the second sequence be $y_{1}, y_{2}\left(y_{1}, y_{2} \in \mathrm{N}\right)$. Then the seventh terms of the two sequences are $5 x_{1}+8 x_{2}$ and $5 y_{1}+8 y_{2}$, respectively, and
$$
\begin{array}{l}
5 x_{1}+8 x_{2}=5 y_{1}+8 y_{2} \\
\Rightarrow 5 x_{1}-5 y_{1}=8 y_{2}-8 x_{2} \\
\Rightarrow x_{1}=y_{1}(\bmod 8), x_{2}=y_{2}(\bmod 5) .
\end{array}
$$

To make $N$ the smallest, thus,
$$
x_{1}=0, x_{2}=13, y_{1}=8, y_{2}=8 \text {. }
$$

Therefore, $N_{\text {min }}=104$.