Question

Find the sum of all the three digit natural numbers divisible by both 3 and 4

Answer 1

the smallest three digit number divisible by both 3 & 4 is 108 and the greatest three digit number divisible by both 3 & 4 is 996. Also the number next to 108 which is divisible by both 3 & 4 is 120. This is because LCM of 3 & 4 is 12, so its easy to see that the subsequent numbers in the series will keep increasing by the number 12.
This forms an AP with first term being 108, the last term being 996. Applying the formulas for Sum of an AP you'll get 41400 as the answer.