an integer w is divisible by 2,3, and 5. What is the next largest internet divisible by these numbers?

Question

I need help on homework question the answer choices are 

(a): w+6

(b): w+10

(c): w+15

(d): w+30

 

Please show me steps 

Answer 1

If w is divisible by 2 and 3 and 5, then there must be some integer value n such that:

    w = n*2*3*5

 

Check this out with values of n = 1, 2, 3, 4, ...

 

That means that w can be 30, 60, 90, 120, ...

      [note: these are the integers that are divisible by 2 and 3 and 5]

 

If w=n*2*3*5 is divisible by 2 and 3 and 5, then the next integer that is divisible by 2 and 3 and 5 is:

     (n+1)*2*3*5

     n+2*3*5 + 2*3*5

       w + 2*3*5

       w + 30

Answer 2

The next largest integer divisible by 2, 3, 5 would be :

w + (2)*(3)*(5) = w + 30