Find the sum of all natural numbers from 1 and 100 which are divisible by 4 or 5.
Question:

Find the sum of all natural numbers from 1 and 100 which are divisible by 4 or 5.

 

Solution:

To Find: The sum of all natural numbers from 1 to 100 which are divisible by 4 or 5.

A number divisible by both 4 and 5 should be divisible by 20 which is the LCM of 4 and 5.

Sum of numbers divisible by 4 OR 5 = Sum of numbers divisible by 4 + Sum of numbers divisible by 5 – Sum of numbers divisible by both 4 and 5.

Sum of numbers divisible by $4=4+8+12+\ldots 100$

$=4(1+2+3+\ldots 25)=4 \times \frac{25}{2}[2+24]=50 \times 26=1800$ Sum of numbers

divisible by $5=5+10+15+20+\ldots 100$

$=5(1+2+3+. .20)$

$=5 \times \frac{20}{2}[2+19]=50 \times 21=1050$ Sum of numbers divisible by $20=20+$

$40+60 \ldots 100$

$=20(1+2+3+4+5)=20 \times 15=300$

Required sum $=1800+1050-300=2550$

Sum of numbers which are divisible by 4 or 5 is 2550

 

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