Find the sum of all natural numbers from 1 and 100 which are divisible by 4 or 5.
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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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,