Question

Find the sum of all the integers lying between -11 and 17 which are divisible by 2 and 3 both.

Answer 1

First, we have to find the integers between -11 and 17 which are divisible by 2. Those are:
-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12, 14, 16

Now, we need to find the integers between -11 and 17 which are divisible by 3. Those are:
-9, -6, -3, 0, 3, 6, 9, 12, 15

Integers which are divisible by both 2 and 3 are the common integers in the above mentioned set of integers.

Therefore, the integers which are divisible by 2 and 3 both, are:
-6, 0, 6 and 12.

The sum of these integers = -6 + 0 + 6 + 12 = 12
Hence the final answer is 12.