Principal period of $\sin\frac{3x}{4}+\cos\frac{2x}{5}$ [duplicate]

The period of $\displaystyle\sin(ax+c)=\frac{2\pi}a$ that of $\displaystyle\cos(bx+d)=\frac{2\pi}b$

Now if $\displaystyle\frac{\dfrac{2\pi}a}{\dfrac{2\pi}b}=\frac ba$ is rational, the period of $\displaystyle\sin(ax+c)+\cos(bx+d)$ will be lcm $\displaystyle\left(\frac{2\pi}b,\frac{2\pi}a\right)$ or its divisor

Hint

Plotting the function is a good idea but your plot is not properly scaled. If you are not able to change the length of the $y$ axis, plot $$20\Big(\sin\frac{3x}{4}+\cos\frac{2x}{5}\Big)$$ and you will visually percieve what lab bhattacharjee means in his good answer.