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    LCM for 2, 7 and 8

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

    What's the Least Common Multiple (LCM) of 2, 7 and 8?

    Answer

    LCM of 2, 7 and 8 is
    56

    (Fifty-six)

    56 is the smallest positive integer that 2, 7 and 8 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 2, 7 and 8 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 2: 2 (exponent form: 2)

    All Prime Factors of 7: 7 (exponent form: 7)

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

    Prime factor278Highest power
    22—2323
    7—7—7

    LCM = 23 × 7 = 56

    Checking the LCM of 2, 7 and 8 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(2, 7) = (2 × 7) ÷ 1 = 14 ÷ 1 = 14

    LCM(14, 8) = (14 × 8) ÷ 2 = 112 ÷ 2 = 56

    LCM(2, 7, 8) = 56

    The pairs may be taken in any order — 7 and 8 first, then 2 — and the answer is the same 56. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 2, 7 and 8?. The LCM of 2, 7 and 8 is 56 — 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
    12714
    22714
    23742
    24728
    25770
    26742
    27714
    27856
    279126
    271070
    2711154
    271284
    2713182
    271414
    2715210
    2716112
    2717238
    2718126
    2719266
    2720140
    272142
    2722154
    2723322
    2724168
    2725350
    2726182
    2727378
    272828
    2729406
    2730210

    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 2, 7 and 8? (The answer is: 56). Enter the first number (e.g. '2'), the second (e.g. '7') and the third (e.g. '8'), 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 2, 7 and 8?

    LCM of 2, 7 and 8 is 56

    How to find the LCM of 2, 7 and 8 by prime factorization?

    Take every prime that appears in 2, 7 and 8 to the highest power it reaches in any one of them and multiply: 2³ × 7 = 56.

    Can you get the LCM of 2, 7 and 8 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 2 and 7 is 14, and the LCM of 14 and 8 is 56 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 56 divisible by 2, 7 and 8?

    Yes, and by definition it is the smallest positive integer that is: 56 ÷ 2, 56 ÷ 7 and 56 ÷ 8 all come out whole. Any other common multiple of 2, 7 and 8 is a multiple of 56.

    See Also