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

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: $\frac{6}{5},\frac{7}{10},\frac{2}{25}$

1. LCM of Numerators ($6,7,2$):
* Prime factorization of $6=2\times 3$
* Prime factorization of $7=7$
* Prime factorization of $2=2$
* $\text{LCM}(6,7,2)=2\times 3\times 7=42$

2. HCF of Denominators ($5,10,25$):
* Factors of $5=5$
* Factors of $10=2\times 5$
* Factors of $25=5\times 5$
* $\text{HCF}(5,10,25)=5$

Substituting the values into the formula:

$$\text{LCM}=\frac{42}{5}$$