Question

The smallest natural number of the form $123X43Y$, which is exactly divisible by $6$ is______

Answer 1

Factor of $6=2,3$

If $123X43Y$ is divisible by $2$ then its unit digit should be $0,2,4,6,8$ and the number for being divisible of $3$, the sum of its digits $(13+X+Y)$ should be divisible by $3$

Hence,

$X+Y=2$

So,

When $X=0,Y=2$

Therefore the number is $1230432.$

Or

When $X=2,Y=0$

Therefore the number is $1232430.$

As per the given condition of the smallest number, the correct answer is $1230432.$

Hence, this is the answer.