Question

Find the least $5$ digit number which is exactly divisible by $12,15$ and $18?$

Answer 1

Find the LCM of $12,15$ and $18.$

It will be $2\times 2\times 3\times 3\times 5=180.$

The smallest $5$ digit number is $10000;$

Now find the multiple of $180$ close to $10000.$

By observation, $180\times 50$ will be $9000$ and $180\times 6=1080;$

Adding both, I.e, $180\times 56=10080;$

Just to check, $180\times 55=9900,$ is a $4$ digit number.

So, $10080$ is the smallest $5$ digit number divisible by $12,15$ and $18.$