The smallest number that is divisible by $4,6,$ and $12$ is ____.

The correct option is A 12
The smallest number divisible by any $2$ or more numbers is the least common multiple (LCM) of the numbers.

Multiples of $4:4,8,12,16,20,24,28,32,36,40......$

Multiples of $6:6,12,18,24,30,36,42,48,54,60.........$

Multiples of $12:12,24,36,48,60,72,84,96,108,\mathrm{120...}$

As you can see, $12$ is the smallest multiple that is common to all three numbers.

So, the LCM of $4,6,$ and $12$ is $12.$

Hence, The smallest number that is divisible by $4,6$ and $12$ is $12.$