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    LCM for 3, 7 and 8

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

    What's the Least Common Multiple (LCM) of 3, 7 and 8?

    Answer

    LCM of 3, 7 and 8 is
    168

    (One hundred sixty-eight)

    168 is the smallest positive integer that 3, 7 and 8 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 3, 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 3: 3 (exponent form: 3)

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

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

    Prime factor378Highest power
    2——2323
    33——3
    7—7—7

    LCM = 23 × 3 × 7 = 168

    Checking the LCM of 3, 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(3, 7) = (3 × 7) ÷ 1 = 21 ÷ 1 = 21

    LCM(21, 8) = (21 × 8) ÷ 1 = 168 ÷ 1 = 168

    LCM(3, 7, 8) = 168

    The pairs may be taken in any order — 7 and 8 first, then 3 — and the answer is the same 168. That is exactly why the two routes on this page agree.

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    What is the LCM of 3, 7 and 8?. The LCM of 3, 7 and 8 is 168 — 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
    13721
    23742
    33721
    34784
    357105
    36742
    37721
    378168
    37963
    3710210
    3711231
    371284
    3713273
    371442
    3715105
    3716336
    3717357
    3718126
    3719399
    3720420
    372121
    3722462
    3723483
    3724168
    3725525
    3726546
    3727189
    372884
    3729609
    3730210

    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, 7 and 8? (The answer is: 168). Enter the first number (e.g. '3'), 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 3, 7 and 8?

    LCM of 3, 7 and 8 is 168

    How to find the LCM of 3, 7 and 8 by prime factorization?

    Take every prime that appears in 3, 7 and 8 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

    Can you get the LCM of 3, 7 and 8 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 3 and 7 is 21, and the LCM of 21 and 8 is 168 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 168 divisible by 3, 7 and 8?

    Yes, and by definition it is the smallest positive integer that is: 168 ÷ 3, 168 ÷ 7 and 168 ÷ 8 all come out whole. Any other common multiple of 3, 7 and 8 is a multiple of 168.

    See Also