No. of odd proper divisors of $3^{\mathrm{p}}\cdot 6^{\mathrm{m}}\cdot {21}^{\mathrm{n}}$ is

$$\begin{gathered} 3^{\mathrm{p}}\cdot 6^{\mathrm{m}}\cdot {21}^{\mathrm{n}} \\ \Rightarrow 3^p\left(2^m{3}^m\right)3^n{7}^n \\ \Rightarrow 2^m{3}^{p+m+n}{7}^n \end{gathered}$$

No of odd proper divisors= No of odd divisors except 1

No. of odd proper divisors $=(\mathrm{P}+\mathrm{m}+\mathrm{n}+1)(\mathrm{n}+1)-1$