Question

What is the smallest number you have to add to $100000$ to get a multiple of $1234$?

Answer 1

Let us first divide $100000$ by $1234$ as shown above:

Now since $1234-46=1188$, therefore,

$100000+1188=101188=1234\times 82$

Hence, $1188$ is the smallest number we have to add to $100000$ to get a multiple of $1234$.