Given, the range of natural numbers is from 100 to 300.

We have to find the sum of all natural numbers which are exactly divisible by 4 or 5.

Divisibility Rule:

To check if a number is divisible by 4, we can check if its last two digits are divisible by 4.

To check if a number is divisible by 5, we can check if its last digit is either 0 or 5.

Approach:

We will find the sum of all natural numbers which are exactly divisible by 4 and then add it with the sum of all natural numbers which are exactly divisible by 5.

We will use the formula to find the sum of natural numbers from 1 to n, which is n*(n+1)/2.

We will then add the sum of natural numbers which are exactly divisible by both 4 and 5, which we have counted twice while finding the sum of natural numbers which are exactly divisible by 4 and 5.

Calculation:

Numbers which are exactly divisible by 4:

The first number which is exactly divisible by 4 in the given range is 100.

The last number which is exactly divisible by 4 in the given range is 300.

We can find the number of terms using the formula (last term - first term)/common difference + 1.

Here, the common difference is 4.

Number of terms = (300-100)/4 + 1 = 51.

The sum of first and last term = 100 + 300 = 400.

The sum of natural numbers which are exactly divisible by 4 = 51*(100+300)/2 = 7650.

Numbers which are exactly divisible by 5:

The first number which is exactly divisible by 5 in the given range is 100.

The last number which is exactly divisible by 5 in the given range is 300.

We can find the number of terms using the formula (last term - first term)/common difference + 1.

Here, the common difference is 5.

Number of terms = (300-100)/5 + 1 = 41.

The sum of first and last term = 100 + 300 = 400.

The sum of natural numbers which are exactly divisible by 5 = 41*(100+300)/2 = 6150.

Numbers which are exactly divisible by both 4 and 5:

The first number which is exactly divisible by both 4 and 5 in the given range is 100.

The last number which is exactly divisible by both 4 and 5 in the given range is 300.

We can find the number of terms using the formula (last term - first term)/common difference + 1.

Here, the common difference is 20 (LCM of 4 and 5).

Number of terms = (300-100)/20 + 1 = 11.

The sum of first and last term = 100 + 300 = 400.

The sum of natural numbers which are exactly divisible by both 4 and 5 = 11*(100+300)/2 = 2200.

Sum of all natural numbers which are exactly divisible by 4 or 5 = sum of natural numbers which are exactly divisible by 4 + sum of natural numbers which are exactly divisible by 5 - sum of natural numbers which are exactly divisible by both 4 and 5.

Sum of all