Question

The period of the function $f\left(x\right)=\sin 2\pi x+\sin \frac{\pi x}{3}+\sin \frac{\pi x}{5}$ is

• A. $2$
• B. $6$
• C. $15$
• D. $30$

Answer 1

The correct option is D $30$

Given that $f\left(x\right)=\sin 2\pi x+\sin \frac{\pi x}{3}+\sin \frac{\pi x}{5}$
Period of $f\left(x\right)=$ LCM ( period of $\sin 2\pi x,\sin \frac{\pi x}{3},\sin \frac{\pi x}{5})$
Period of $f\left(x\right)=$ LCM $(1,6,10)=30$
Hence, option 'D' is correct.