Utilorca
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LCM and GCF calculator

LCM and GCF calculator by Utilorca (utilorca.com): free, no sign-up, runs in your browser. Enter two or more whole numbers to get the least common multiple and the greatest common factor at once, with each number’s prime factorization and the division (ladder) method.

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).

    Private by design: your files are processed on your device and never uploaded.

    How to use it

    1. Type the numbers separated by spaces or commas, for example 12 18 30.
    2. Read the LCM and the GCF at the top.
    3. Follow the prime factorization and the division table to see how each one is found.

    Questions and answers

    How do you find the LCM with prime factorization?

    Factor each number into primes, take every prime that appears, each with its highest power, and multiply. 12 = 2² × 3 and 18 = 2 × 3², so LCM = 2² × 3² = 36.

    How do you find the GCF?

    Take only the primes that appear in every number, each with its lowest power. For 12 and 18 that is 2 × 3 = 6. Two numbers with GCF 1 are called relatively prime.

    Is there a shortcut for two numbers?

    Yes: LCM × GCF = the product of the two numbers. For 12 and 18, 36 × 6 = 216 = 12 × 18. This does not work for three or more numbers.

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