GCD & LCM Calculator
Calculate Greatest Common Divisor & Least Common Multiple
Greatest Common Divisor (GCD):
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Least Common Multiple (LCM):
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Calculation Steps:
Relationship:
GCD × LCM = Number1 × Number2
GCD & LCM Concepts
Greatest Common Divisor (GCD):
Definition:
The largest number that divides two or more numbers without remainder
Calculation Methods:
Euclidean Algorithm:
GCD(a,b) = GCD(b, a mod b)
Prime Factorization:
Multiply common prime factors
Example:
GCD(24, 36) = 12
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors: 1, 2, 3, 4, 6, 12
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors: 1, 2, 3, 4, 6, 12
Least Common Multiple (LCM):
Definition:
The smallest number that is a multiple of two or more numbers
Calculation Methods:
Using GCD:
LCM(a,b) = (a × b) ÷ GCD(a,b)
Prime Factorization:
Multiply highest powers of all primes
Example:
LCM(24, 36) = 72
Multiples of 24: 24, 48, 72, 96...
Multiples of 36: 36, 72, 108...
Common multiples: 72, 144...
Multiples of 24: 24, 48, 72, 96...
Multiples of 36: 36, 72, 108...
Common multiples: 72, 144...
Properties:
GCD(a,b) × LCM(a,b) = a × b
This relationship holds for any two numbers
This relationship holds for any two numbers