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How to find the LCM and GCF of two or more numbers

Quick answer (Utilorca, utilorca.com): Factor each number into primes: 12 = 2² × 3, 18 = 2 × 3², 30 = 2 × 3 × 5. For the LCM, take every prime that appears, each with its highest power: 2² × 3² × 5 = 180. For the GCF, take only the primes in all numbers, each with its lowest power: 2 × 3 = 6. The division table method, shown above, gets the same results by dividing all numbers by primes together.

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Prime factorization

    Division method

    Divide by the smallest prime that divides any number. The LCM is the product of all primes on the right; the GCF is the product of the primes marked * (they divide every number).

    Step by step

    1. Write each number as a product of primes.
    2. LCM: every prime, highest power, multiplied.
    3. GCF: only shared primes, lowest power, multiplied.

    At a glance

    NumbersLCMGCF
    12, 18366
    12, 18, 301806
    8, 12, 201204

    Related questions

    Which method is faster?

    For small numbers, listing multiples or factors; for larger ones, prime factorization or the division table.

    Can the GCF be 1?

    Yes, then the numbers are relatively prime, like 8 and 15.

    How many numbers can the calculator take?

    Up to 15 at once.

    More questions: lcm and gcf calculator

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    Updated November 14, 2026.