A function f(x) is defined as $f\left(x\right)=\left\{\begin{array}{cc}{x}^m\sin \frac{1}{x},& x\ne 0,m\in N\\ 0,& \text{ if }x=0\end{array}\right.$ 

The least value of m for which f(x) is continuous at $x=0$ is _____

$$\begin{gathered} Given function \\ f\left(x\right)=\left\{\begin{array}{l}{x}^{m }\sin \left(\frac{1}{x}\right),x\ne 0,m\in N\\ 0 if x=0\end{array}\right. \\ f\left(x\right) is continuous at x=0 if \underset{x\to 0}{\lim }f\left(x\right)=f\left(0\right) \\ \Rightarrow \underset{x\to 0}{\lim }{x}^{m }\sin \left(\frac{1}{x}\right)=0 \\ the above limit will become zero for all values m>0 \\ Here m\in N,so least value of m=1 \end{gathered}$$