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    LCM for 7, 10 and 14

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

    What's the Least Common Multiple (LCM) of 7, 10 and 14?

    Answer

    LCM of 7, 10 and 14 is
    70

    (Seventy)

    70 is the smallest positive integer that 7, 10 and 14 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 7, 10 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 7: 7 (exponent form: 7)

    All Prime Factors of 10: 2 × 5 (exponent form: 2 × 5)

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

    Prime factor71014Highest power
    2—222
    5—5—5
    77—77

    LCM = 2 × 5 × 7 = 70

    Checking the LCM of 7, 10 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(7, 10) = (7 × 10) ÷ 1 = 70 ÷ 1 = 70

    LCM(70, 14) = (70 × 14) ÷ 14 = 980 ÷ 14 = 70

    LCM(7, 10, 14) = 70

    The pairs may be taken in any order — 10 and 14 first, then 7 — and the answer is the same 70. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 7, 10 and 14?. The LCM of 7, 10 and 14 is 70 — 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
    171070
    271070
    3710210
    4710140
    571070
    6710210
    771070
    7810280
    7910630
    7101070
    71011770
    71012420
    71013910
    7101470
    71015210
    71016560
    710171,190
    71018630
    710191,330
    71020140
    71021210
    71022770
    710231,610
    71024840
    71025350
    71026910
    710271,890
    71028140
    710292,030
    71030210

    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 7, 10 and 14? (The answer is: 70). Enter the first number (e.g. '7'), the second (e.g. '10') 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 7, 10 and 14?

    LCM of 7, 10 and 14 is 70

    How to find the LCM of 7, 10 and 14 by prime factorization?

    Take every prime that appears in 7, 10 and 14 to the highest power it reaches in any one of them and multiply: 2 × 5 × 7 = 70.

    Can you get the LCM of 7, 10 and 14 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 7 and 10 is 70, and the LCM of 70 and 14 is 70 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 70 divisible by 7, 10 and 14?

    Yes, and by definition it is the smallest positive integer that is: 70 ÷ 7, 70 ÷ 10 and 70 ÷ 14 all come out whole. Any other common multiple of 7, 10 and 14 is a multiple of 70.

    See Also