Problem 627

6. Given that $F_{1}, F_{2}$ are the common foci of an ellipse and a hyperbola, and $\mathrm{P}$ is one of their common points, with $\angle F_{1} P F_{2}=60^{\circ}$, then the minimum value of the product of the eccentricities of the ellipse and the hyperbola is
A、 $\frac{\sqrt{3}}{3}$
B、 $\frac{\sqrt{3}}{2}$
C、 1
D、 $\sqrt{3}$