Identifying the Multiples of 12

12 is a multiple of 3 and 4. Therefore, the multiples of 12 must be divisible by 3 and 4. We have learned that

If the sum of the digits of a number is a multiple of 3, then the number must also a multiple of 3.

and also

If the first two digits of a number is a multiple of 4, then the number if a multiple of 4.

We can use these two rules to tell if a number is a multiple of 12.

For example:
Is 762288 a multiple of 12?

The sum of the digit:
7 + 6 + 2 + 2 + 8 + 8 = 33

33 is divisible by 3, hence 762288 is a multiple of 3.

The first two digits of 762288 is 88, and 88 is a multiple of 4, hence 762288 is a multiple of 4.

Since 762288 is a multiple of 3 and 4, hence it must also a multiple of 12.

Let's see another example:
Is 7365436 divisible by 12?

The first two digits is 36, and 36 is a multiple of 4, hence 7365436 is a multiple of 4.

The sum of the digit:
7 + 3 + 6 + 5 + 4 + 3 + 6 = 34

34 is not divisible by 3, hence 765436 is not a multiple of 3.

Therefore 7365436 is not divisible by 12.