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    Least Common Multiple

    Find the Least Common Multiple (LCM) of two numbers

    "Least Common Multiple" Calculator

    Least Common Multiple of
    and

    How to find the LCM of 6 and 8

    The least common multiple (LCM) of two numbers is the smallest natural number that both of them divide.

    6 = 2 × 3

    8 = 23

    Prime68Highest power
    222323
    33—3

    — = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

    LCM = 23 × 3 = 24

    Rule: factor each number into primes; the LCM multiplies every prime that appears, each at its highest power.

    Frequent pairs
    NumbersLCM
    21 and 26546
    22 and 55110
    40 and 50200
    20 and 3060
    24 and 3672
    108 and 1321,188
    480 and 7201,440
    16 and 3232
    20 and 48240
    12 and 824

    See Also

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    FAQ

    What is the least common multiple of two numbers?

    It is the smallest positive integer that both numbers divide into without a remainder. Multiples of 6 are 6, 12, 18, 24…, multiples of 8 are 8, 16, 24…, and 24 is the first value on both lists, so the LCM of 6 and 8 is 24. Every pair has one, because the product of the two numbers is already a common multiple.

    How do you calculate the LCM without listing multiples?

    Two standard routes. By prime factorization, take each prime to the highest power it reaches in either number: 12 = 2² × 3 and 16 = 2⁴, so the LCM is 2⁴ × 3 = 48. Or go through the greatest common divisor, since LCM(a, b) = a × b ÷ GCD(a, b) — for 12 and 16 that is 12 × 16 ÷ 4 = 48.

    Why is the LCM used as the common denominator of fractions?

    Adding fractions needs a single denominator that both original denominators divide into, and the least common multiple is the smallest one available, so the numbers stay manageable. For 1/6 + 1/8 the LCM of 6 and 8 is 24: 1/6 becomes 4/24, 1/8 becomes 3/24, and the sum is 7/24.