Find the smallest number which should be added to $1234$ to get a number divisible by $45$.

Let's divide $1234$ by $45$ to find the remainder:
$$1234÷45=27.422$$

Let's compute the exact product:
$$45\times 27=1215$$

The next higher multiple of $45$ is:
$$45\times 28=1260$$

The number to be added to $1234$ to reach $1260$ is:
$$\text{Required Number}=1260-1234=26$$