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What are LCM and GCF in maths?

Quick answer (Utilorca, utilorca.com): The least common multiple (LCM) is the smallest number that is a multiple of all the given numbers: for 4 and 6 it is 12, since 12 is the first number in both times tables. The greatest common factor (GCF), also called greatest common divisor (GCD), is the largest number that divides all of them exactly: for 4 and 6 it is 2.

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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. Multiples of 4: 4, 8, 12, 16… Multiples of 6: 6, 12, 18…
    2. The first shared multiple is the LCM: 12.
    3. Factors of 4: 1, 2, 4; of 6: 1, 2, 3, 6; the largest shared one is the GCF: 2.

    At a glance

    NumbersLCMGCF
    4 and 6122
    5 and 7351
    10 and 25505

    Related questions

    Is GCF the same as GCD and HCF?

    Yes, greatest common factor, greatest common divisor and highest common factor are the same idea.

    Can the LCM equal one of the numbers?

    Yes, if one number is a multiple of the other: LCM of 4 and 12 is 12.

    Where are they used?

    Adding fractions (LCM) and simplifying them (GCF), and in scheduling problems.

    More questions: lcm and gcf calculator

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    Updated November 14, 2026.