Find the LCM of $\frac{6}{5}$, $\frac{7}{10}$, $\frac{2}{25}$.

The Least Common Multiple (LCM) of fractions is calculated using the standard formula:
$$\text{LCM of Fractions}=\frac{\text{LCM of Numerators}}{\text{HCF of Denominators}}$$

The numerators are $6,7,2$ and the denominators are $5,10,25$.

1. **Find the LCM of the numerators $(6,7,2)$ **:
* Factors of $6=2\times 3$
* Factors of $7=7$
* Factors of $2=2$

$$\text{LCM}(6,7,2)=2\times 3\times 7=42$$

2. **Find the HCF of the denominators $(5,10,25)$ **:
* Factors of $5=5$
* Factors of $10=2\times 5$
* Factors of $25=5\times 5$

$$\text{HCF}(5,10,25)=5$$

Combining these components:

$$\text{LCM of the given fractions}=\frac{42}{5}$$