Finding GCD
The GCD is the largest positive integer that divides all given numbers without remainder. Use the Euclidean algorithm for efficient calculation: repeatedly divide and take remainders until you reach 0.
LCM & GCD Calculator
LCM and GCD are the foundation of fraction arithmetic — adding fractions requires LCM to find the common denominator, while simplifying fractions requires GCD to reduce to lowest terms. Beyond basic math, GCD (computed via Euclid's algorithm) is used in cryptography to check coprimality of RSA keys, in gear ratio calculations in mechanical engineering, and in scheduling problems where you need to find when recurring events coincide. Enter up to multiple numbers at once for batch computation.
star
4.8
calendar_today
Updated:
LCM & GCD Calculator calculator
calculate
LCM & GCD Calculator
Enter 2 or more positive integers
Parsed Numbers
12, 18
Key Relationship
LCM × GCD = a × b
For two numbers a and b
functions
Results
GCD (Greatest Common Divisor)
6
Also called HCF (Highest Common Factor)
LCM (Least Common Multiple)
36
Smallest number divisible by all inputs
Verification
GCD × LCM = 6 × 36 = 216 = 12 × 18 ✓
Prime Factorization
12 = 2² × 3
18 = 2 × 3²
How it works:
GCD: Take lowest powers → 2¹ × 3¹ = 6
LCM: Take highest powers → 2² × 3² = 36
Euclidean Algorithm (GCD)
18 = 12 × 1 + 6
12 = 6 × 2 + 0
→ GCD = 6
lightbulb Tips
- •LCM × GCD = a × b
- •GCD = HCF (same thing)
- •Use Euclidean algorithm
- •GCD=1 means coprime
calculate Reference
Common GCDs
GCD(12,18)=6GCD(24,36)=12
GCD(15,25)=5GCD(48,60)=12
Key Formulas
LCM × GCD = a × b
LCM = (a × b) / GCD
How to Use the LCM & GCD Calculator
edit
Enter Numbers
Input two or more positive integers separated by commas.
calculate
Choose Calculation
Select LCM, GCD, or both calculations.
tune
Select Method
View Euclidean algorithm, prime factorization, or both.
visibility
View Results
See LCM/GCD with step-by-step solution.
The Formula
GCD is the largest number that divides all given numbers. LCM is the smallest number divisible by all given numbers.
LCM(a,b) × GCD(a,b) = a × b
lightbulb Variables Explained
- GCD Greatest Common Divisor
- LCM Least Common Multiple
- HCF Highest Common Factor (same as GCD)
tips_and_updates Pro Tips
1
GCD (Greatest Common Divisor) is also called HCF (Highest Common Factor)
2
LCM × GCD = Product of the two numbers (for 2 numbers)
3
If GCD = 1, the numbers are coprime (no common factors)
4
Use GCD to simplify fractions: divide numerator and denominator by their GCD
5
LCM is useful for finding common denominators when adding fractions
6
The Euclidean algorithm efficiently finds GCD by repeated division
Calculate the Least Common Multiple (LCM) and Greatest Common Divisor (GCD/HCF) with step-by-step solutions using Euclidean algorithm and prime factorization.
Finding LCM
The LCM is the smallest positive integer divisible by all given numbers. Calculate using prime factorization (take highest powers) or the formula: LCM = (a × b) / GCD.