The ratio of two numbers is $5:6$ and their HCF is $12$. Their LCM is

Let the two numbers be $5x$ and $6x$, where $x$ represents their highest common factor ($\text{HCF}$).Given $\text{HCF}=x=12$.The numbers are:
$$\text{First number}=5\times 12=60$$
$$\text{Second number}=6\times 12=72$$
The formula for the least common multiple ($\text{LCM}$) of two numbers ratio-wise is:
$$\text{LCM}={\text{Ratio}}_1\times {\text{Ratio}}_2\times \text{HCF}$$
$$\text{LCM}=5\times 6\times 12=30\times 12=360$$