Sudad, let's say two numbers are a and b, and a > b. The difference between the two numbers is a - b.

Hi Joelene,

Although each of the two numbers is divisible by 2, 3, and 4, we did not know whether the difference of the two numbers was also divisible by 2, 3, and 4. We had to prove that, and did so by showing that their difference is divisible by 12, which is same as saying the difference is divisible by 2, 3, and 4 since the factors of 12 are 2, 3, and 4.

Note: Instead of using the 12, we can carry the factors 2, 3, and 4 throughout the proof (although this makes the proof messy, perhaps it's clearer):

Let the first number be represented as (2)(3)(4)a and the second number as (2)(3)(4)b. Assuming a > b, the difference between the two numbers is (2)(3)(4)a − (2)(3)(4)b = (2)(3)(4)(a − b). Observe that this number is also a multiple of (2)(3)(4). Hence, the answer must also be divisible by (2)(3)(4). Since 72 is the only answer-choice divisible by (2)(3)(4), the answer is (B).

Nova Press