Question

What is the smallest multiple of 18 of the form 2A945B, where A and B are digits?

Answer 1

`219456`

Explanation:

It must end in
`0,2,4,6,8` (divisible by 2 rule) and the digits must sum to a multiple of 9(divisible by 9 rule).

The digit sum is
`2+A+9+4+5+B=20+A+B`.

We want to make
`A` as low as possible because it's a higher digit than
`B`.

If
`A` is as low as possible, we have that the sum is
`20+0+7=27`. Uh-oh.
`B` has to be even! So
`A=0` doesn't work.

If
`A=1`, we have that the sum is
`20+1+6=27`. Yay!

So, the answer is
`\boxed{219456}`