For a number to be divisible by 5,250 it must contain a factorization string of 5,250 (7 × 3 × 5 × 5 × 2 × 5) in its own factorization string.

So the factorization string of the number we're looking for is 7 × 3 × 5 × 5 × 2 × 5 × .....

Let us see which prime factors of 420 it already contains:

**7** ×

**3** × 5 × 5 ×

**2** ×

**5** × ....

420 =

**2** ×

**3** ×

**7** × 2 ×

**5**We see that it contains 2 × 3 × 7 × 5, but doesn't contain another 2. So we must add at least one more prime factor "2" to the factorization string: 7 × 3 × 5 × 5 × 2 × 5

**× 2**.

Since we are looking for the smallest number, we must add no more factors to it.

7 × 3 × 5 × 5 × 2 × 5 × 2 = (7 × 3 × 5 × 5 × 2 × 5) × 2 = 5,250 × 2 = 10,500.

If we added a multiplier 3, 5 or 7 to the string instead of 2, then the resulting number would NOT be divisible by 420, because it would NOT contain enough prime factors of 420.

This question is solely about finding the least common multiple of two numbers. So if you have troubles doing so, you should go over the corresponding section of the guide again (

http://www.800score.com/gmat-guide.html).