The ratio of two numbers is $3:4$ and their L.C.M. is $180$. Find the numbers.

Let the two numbers be $3x$ and $4x$.
The LCM of $3x$ and $4x$ is $12x$.

Given that the LCM is $180$:

$$12x=180$$

$$x=\frac{180}{12}=15$$

Now, calculate the two numbers:

$$\text{First number}=3\times 15=45$$

$$\text{Second number}=4\times 15=60$$

Therefore, the numbers are $45$ and $60$.