Find the Greatest Common Divisor and Least Common Multiple
Prime Factors Intersection Venn Diagram
Shared Prime Factors (overlap) product = GCD (6)Prime Factorizations
Evidence-based guide
GCD (also known as GCF) finds the largest integer that divides all entered numbers without a remainder. LCM finds the smallest positive integer that is a multiple of all entered numbers.
Decompose numbers into prime factor powers. GCD takes the lowest powers of shared primes; LCM takes the highest powers of all primes.
An efficient method for computing the GCD of two numbers by repeated remainder division.
Shows intersection of prime factors of two numbers visually to identify common divisors.
GCD is useful for simplifying fractions or dividing objects into equal groups. LCM is useful for finding common denominators or scheduling recurring synchronized events.
The calculator only operates on positive integers. Fractions, decimals, and negative numbers are excluded.
For example, 12 = 2² × 3 and 18 = 2 × 3². The shared factors are one 2 and one 3. Their product (2 × 3 = 6) is the GCD.
For two numbers, the product of their GCD and LCM equals the product of the numbers themselves: GCD(a, b) × LCM(a, b) = a × b.
Yes. This upgraded calculator supports adding arbitrary rows of inputs or entering a comma-separated list of values.
