SOLUTION: What is the sum of the digits of the smallest positive integer that is divisible by 2, 3, 4, 6, and 7? A)14 B)16 C)9 D)12 E)15

To be divisible by 2 it must have factor 2

So write down what we have so far, which is only a 2 factor: 

2

To be divisible by 3 it must have factor 3 

So write *3 by the 2. So far we have:

2*3

To be divisible by 4=2*2 it must have factor 2 twice. It already has factor 2
once so we just need to write *2 beside 2*3 to have the factor 2 twice:

So we write *2 by the 2*3, and so far we have:

2*3*2 

To be divisible by 6=2*3 it must have factors 2 and 3. It already has those
once so we don't need to write anything else and so far we we still have:

2*3*2

To be divisible by 7 it must have factor 7 

So write *7 by the 2*3*2.  And we end up with

2*3*2*7 = 84

The sum of the digits of 84 is 8+4 or 12, choice D)

Edwin