Find the LCM of $\frac{1}{3},\frac{1}{6},\frac{10}{9},\frac{5}{18}$.

To find the LCM of fractions, we use the formula:
$$\text{LCM of fractions}=\frac{\text{LCM of Numerators}}{\text{HCF of Denominators}}$$

Given fractions: $\frac{1}{3},\frac{1}{6},\frac{10}{9},\frac{5}{18}$

* Numerators: $1,1,10,5$

$$\text{LCM}(1,1,10,5)=10$$

* Denominators: $3,6,9,18$

$$\text{HCF}(3,6,9,18)=3$$

Therefore,

$$\text{LCM of fractions}=\frac{10}{3}$$