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    LCM for 12, 14 and 20

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

    What's the Least Common Multiple (LCM) of 12, 14 and 20?

    Answer

    LCM of 12, 14 and 20 is
    420

    (Four hundred twenty)

    420 is the smallest positive integer that 12, 14 and 20 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 12, 14 and 20 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 14: 2 × 7 (exponent form: 2 × 7)

    All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)

    Prime factor121420Highest power
    22222222
    33——3
    5——55
    7—7—7

    LCM = 22 × 3 × 5 × 7 = 420

    Checking the LCM of 12, 14 and 20 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, 14) = (12 × 14) ÷ 2 = 168 ÷ 2 = 84

    LCM(84, 20) = (84 × 20) ÷ 4 = 1,680 ÷ 4 = 420

    LCM(12, 14, 20) = 420

    The pairs may be taken in any order — 14 and 20 first, then 12 — and the answer is the same 420. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 12, 14 and 20?. The LCM of 12, 14 and 20 is 420 — 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
    51214420
    6121484
    7121484
    81214168
    91214252
    101214420
    111214924
    12121484
    1213141,092
    12141484
    121415420
    121416336
    1214171,428
    121418252
    1214191,596
    121420420
    12142184
    121422924
    1214231,932
    121424168
    1214252,100
    1214261,092
    121427756
    12142884
    1214292,436
    121430420
    1214312,604
    121432672
    121433924
    1214341,428

    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, 14 and 20? (The answer is: 420). Enter the first number (e.g. '12'), the second (e.g. '14') and the third (e.g. '20'), 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, 14 and 20?

    LCM of 12, 14 and 20 is 420

    How to find the LCM of 12, 14 and 20 by prime factorization?

    Take every prime that appears in 12, 14 and 20 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 7 = 420.

    Can you get the LCM of 12, 14 and 20 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 12 and 14 is 84, and the LCM of 84 and 20 is 420 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 420 divisible by 12, 14 and 20?

    Yes, and by definition it is the smallest positive integer that is: 420 ÷ 12, 420 ÷ 14 and 420 ÷ 20 all come out whole. Any other common multiple of 12, 14 and 20 is a multiple of 420.

    See Also