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    LCM for 12, 16 and 18

    "Least Common Multiple of 3 Numbers" Calculator
    Least Common Multiple of
    ,
    and

    What's the Least Common Multiple (LCM) of 12, 16 and 18?

    Answer

    LCM of 12, 16 and 18 is
    144

    (One hundred forty-four)

    144 is the smallest positive integer that 12, 16 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 12, 16 and 18 by Prime Factorization

    Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

    All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

    All Prime Factors of 16: 2 × 2 × 2 × 2 (exponent form: 24)

    All Prime Factors of 18: 2 × 3 × 3 (exponent form: 2 × 32)

    Prime factor121618Highest power
    22224224
    33—3232

    LCM = 24 × 32 = 144

    Checking the LCM of 12, 16 and 18 Two Numbers at a Time

    The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

    LCM(a, b) = (a × b) ÷ GCD(a, b)

    LCM(12, 16) = (12 × 16) ÷ 4 = 192 ÷ 4 = 48

    LCM(48, 18) = (48 × 18) ÷ 6 = 864 ÷ 6 = 144

    LCM(12, 16, 18) = 144

    The pairs may be taken in any order — 16 and 18 first, then 12 — and the answer is the same 144. That is exactly why the two routes on this page agree.

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    What is the LCM of 12, 16 and 18?. The LCM of 12, 16 and 18 is 144 — the smallest number all three divide with no remainder. Step-by-step solution for three numbers.
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    LCM Table

    Number 1Number 2Number 3LCM
    3121648
    4121648
    51216240
    6121648
    71216336
    8121648
    91216144
    101216240
    111216528
    12121648
    121316624
    121416336
    121516240
    12161648
    121617816
    121618144
    121619912
    121620240
    121621336
    121622528
    1216231,104
    12162448
    1216251,200
    121626624
    121627432
    121628336
    1216291,392
    121630240
    1216311,488
    12163296

    About "Least Common Multiple of 3 Numbers" Calculator

    This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 12, 16 and 18? (The answer is: 144). Enter the first number (e.g. '12'), the second (e.g. '16') and the third (e.g. '18'), then hit the 'Calculate' button.
    The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
    "Least Common Multiple of 3 Numbers" Calculator
    Least Common Multiple of
    ,
    and

    FAQ

    What's the Least Common Multiple (LCM) of 12, 16 and 18?

    LCM of 12, 16 and 18 is 144

    How to find the LCM of 12, 16 and 18 by prime factorization?

    Take every prime that appears in 12, 16 and 18 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² = 144.

    Can you get the LCM of 12, 16 and 18 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 12 and 16 is 48, and the LCM of 48 and 18 is 144 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 144 divisible by 12, 16 and 18?

    Yes, and by definition it is the smallest positive integer that is: 144 ÷ 12, 144 ÷ 16 and 144 ÷ 18 all come out whole. Any other common multiple of 12, 16 and 18 is a multiple of 144.

    See Also