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    LCM for 10, 12 and 14

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

    What's the Least Common Multiple (LCM) of 10, 12 and 14?

    Answer

    LCM of 10, 12 and 14 is
    420

    (Four hundred twenty)

    420 is the smallest positive integer that 10, 12 and 14 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 10, 12 and 14 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 10: 2 × 5 (exponent form: 2 × 5)

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

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

    Prime factor101214Highest power
    2222222
    3—3—3
    55——5
    7——77

    LCM = 22 × 3 × 5 × 7 = 420

    Checking the LCM of 10, 12 and 14 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(10, 12) = (10 × 12) ÷ 2 = 120 ÷ 2 = 60

    LCM(60, 14) = (60 × 14) ÷ 2 = 840 ÷ 2 = 420

    LCM(10, 12, 14) = 420

    The pairs may be taken in any order — 12 and 14 first, then 10 — and the answer is the same 420. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 10, 12 and 14?. The LCM of 10, 12 and 14 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
    1101260
    2101260
    3101260
    4101260
    5101260
    6101260
    71012420
    81012120
    91012180
    10101260
    101112660
    10121260
    101213780
    101214420
    10121560
    101216240
    1012171,020
    101218180
    1012191,140
    10122060
    101221420
    101222660
    1012231,380
    101224120
    101225300
    101226780
    101227540
    101228420
    1012291,740
    10123060

    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 10, 12 and 14? (The answer is: 420). Enter the first number (e.g. '10'), the second (e.g. '12') and the third (e.g. '14'), 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 10, 12 and 14?

    LCM of 10, 12 and 14 is 420

    How to find the LCM of 10, 12 and 14 by prime factorization?

    Take every prime that appears in 10, 12 and 14 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 7 = 420.

    Can you get the LCM of 10, 12 and 14 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 10 and 12 is 60, and the LCM of 60 and 14 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 10, 12 and 14?

    Yes, and by definition it is the smallest positive integer that is: 420 ÷ 10, 420 ÷ 12 and 420 ÷ 14 all come out whole. Any other common multiple of 10, 12 and 14 is a multiple of 420.

    See Also