$37 \cdot 1$ lattice points refer to points in the plane whose coordinates are integers. The number of lattice points on the line segment with endpoints $(3,17),(48,281)$ (including the endpoints) is 
(A) 2.
(B) 4.
(C) 6.
(D) 16.
(E) 46:
(40th American High School Mathematics Examination, 1989)
［Solution］The slope of the line passing through the two given points is
$$
k=\frac{281-17}{48-3}=\frac{264}{45}=\frac{3 \cdot 2 \cdot 2 \cdot 2 \cdot 11}{3 \cdot 3 \cdot 5}=\frac{3 \cdot 2^{3} \cdot 11}{3^{2} \cdot 5}
$$

Obviously, the only common factor of the numerator and denominator is 3, i.e., $k=\frac{88}{15}$.
Thus, apart from the endpoints, there are only two integer points on the line segment:
and
$$
\begin{array}{l}
(48-15,281-88)=(33,193), \\
(15+3,88+17)=(18,105) .
\end{array}
$$

Therefore, the answer is $(B)$.