To find the numbers that are divisible by both 15 and 21, we need to find the numbers that are divisible by their least common multiple (LCM).

The LCM of 15 and 21 can be found by finding their prime factorizations:
15 = 3 * 5
21 = 3 * 7

The LCM is the product of the highest powers of all the prime factors involved:
LCM(15, 21) = 3 * 5 * 7 = 105

Now, we need to find how many numbers less than 700 are divisible by 105.

Dividing 700 by 105 gives us approximately 6.6667. Since we are looking for whole numbers, we take the floor of this value, which is 6.

So, there are 6 numbers less than 700 that are divisible by both 15 and 21.