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LCM and GCF calculator

Least common multiple and greatest common divisor, with prime factorization.

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2 to 20 positive numbers, separated by spaces or commas.

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LCM

180

For 12, 18 and 30, the LCM is 180 and the GCD is 6.

How this is calculated →
  • GCD (GCF)6
  • 122² × 3
  • 182 × 3²
  • 302 × 3 × 5

How to find the LCM and GCD

The GCD comes from Euclid's algorithm: divide the larger by the smaller and repeat with the remainder until it is zero; the last divisor is the GCD. The LCM of two numbers is a × b ÷ GCD(a, b), applied in turn for more numbers.

With prime factors: the GCD multiplies the shared primes at their lowest power; the LCM multiplies every prime at its highest power. 12 = 2² × 3, 18 = 2 × 3², 30 = 2 × 3 × 5: LCM = 2² × 3² × 5 = 180; GCD = 2 × 3 = 6.

Frequently asked questions

What is the LCM used for?

Adding fractions (it is the common denominator) and finding when repeating events line up, like buses every 12 and 18 minutes.

What is the GCD used for?

Simplifying fractions and splitting things into the largest possible equal groups.

How are LCM and GCD related?

For two numbers, LCM × GCD = a × b.

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