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    LCM for 8, 14 and 21

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

    What's the Least Common Multiple (LCM) of 8, 14 and 21?

    Answer

    LCM of 8, 14 and 21 is
    168

    (One hundred sixty-eight)

    168 is the smallest positive integer that 8, 14 and 21 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 14 and 21 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 8: 2 × 2 × 2 (exponent form: 23)

    All Prime Factors of 14: 2 × 7 (exponent form: 2 × 7)

    All Prime Factors of 21: 3 × 7 (exponent form: 3 × 7)

    Prime factor81421Highest power
    2232—23
    3——33
    7—777

    LCM = 23 × 3 × 7 = 168

    Checking the LCM of 8, 14 and 21 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(8, 14) = (8 × 14) ÷ 2 = 112 ÷ 2 = 56

    LCM(56, 21) = (56 × 21) ÷ 7 = 1,176 ÷ 7 = 168

    LCM(8, 14, 21) = 168

    The pairs may be taken in any order — 14 and 21 first, then 8 — and the answer is the same 168. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 8, 14 and 21?. The LCM of 8, 14 and 21 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
    6814168
    781456
    881456
    8914504
    81014280
    81114616
    81214168
    81314728
    8141456
    81415840
    81416112
    81417952
    81418504
    814191,064
    81420280
    81421168
    81422616
    814231,288
    81424168
    814251,400
    81426728
    814271,512
    8142856
    814291,624
    81430840
    814311,736
    81432224
    814331,848
    81434952
    81435280

    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 8, 14 and 21? (The answer is: 168). Enter the first number (e.g. '8'), the second (e.g. '14') and the third (e.g. '21'), 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 8, 14 and 21?

    LCM of 8, 14 and 21 is 168

    How to find the LCM of 8, 14 and 21 by prime factorization?

    Take every prime that appears in 8, 14 and 21 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

    Can you get the LCM of 8, 14 and 21 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 14 is 56, and the LCM of 56 and 21 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 8, 14 and 21?

    Yes, and by definition it is the smallest positive integer that is: 168 ÷ 8, 168 ÷ 14 and 168 ÷ 21 all come out whole. Any other common multiple of 8, 14 and 21 is a multiple of 168.

    See Also