$x_1(t)=cos(4t+30)$

$x_2(t)=sin(t)$

$x_3(t)=e^{j5t}$

$v(t)=x_1(t)+x_3(t)+x_3(t)$

The objective is to find the fundamental period for the resultant signal $v(t)$ :

The period for $x_1(t)$ is $T_1=$

The period for $x_2(t)$ is $T_2=$

The period for $x_3(t)$ is $T_3=$

Taking $T_1$ as reference:

The ratio of $\frac{T_1}{T_2}$ is: $$

The ratio of $\frac{T_1}{T_3}$ is: $$

The fundamental period for $v(t)$ is: $$