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    LCM for 3, 8 and 12

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

    What's the Least Common Multiple (LCM) of 3, 8 and 12?

    Answer

    LCM of 3, 8 and 12 is
    24

    (Twenty-four)

    24 is the smallest positive integer that 3, 8 and 12 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 3, 8 and 12 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 3: 3 (exponent form: 3)

    All Prime Factors of 8: 2 × 2 × 2 (exponent form: 23)

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

    Prime factor3812Highest power
    2—232223
    33—33

    LCM = 23 × 3 = 24

    Checking the LCM of 3, 8 and 12 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(3, 8) = (3 × 8) ÷ 1 = 24 ÷ 1 = 24

    LCM(24, 12) = (24 × 12) ÷ 12 = 288 ÷ 12 = 24

    LCM(3, 8, 12) = 24

    The pairs may be taken in any order — 8 and 12 first, then 3 — and the answer is the same 24. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 3, 8 and 12?. The LCM of 3, 8 and 12 is 24 — 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
    13824
    23824
    33824
    34824
    358120
    36824
    378168
    38824
    38972
    3810120
    3811264
    381224
    3813312
    3814168
    3815120
    381648
    3817408
    381872
    3819456
    3820120
    3821168
    3822264
    3823552
    382424
    3825600
    3826312
    3827216
    3828168
    3829696
    3830120

    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 3, 8 and 12? (The answer is: 24). Enter the first number (e.g. '3'), the second (e.g. '8') and the third (e.g. '12'), 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 3, 8 and 12?

    LCM of 3, 8 and 12 is 24

    How to find the LCM of 3, 8 and 12 by prime factorization?

    Take every prime that appears in 3, 8 and 12 to the highest power it reaches in any one of them and multiply: 2³ × 3 = 24.

    Can you get the LCM of 3, 8 and 12 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 3 and 8 is 24, and the LCM of 24 and 12 is 24 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 24 divisible by 3, 8 and 12?

    Yes, and by definition it is the smallest positive integer that is: 24 ÷ 3, 24 ÷ 8 and 24 ÷ 12 all come out whole. Any other common multiple of 3, 8 and 12 is a multiple of 24.

    See Also