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    LCM for 10, 14 and 20

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

    What's the Least Common Multiple (LCM) of 10, 14 and 20?

    Answer

    LCM of 10, 14 and 20 is
    140

    (One hundred forty)

    140 is the smallest positive integer that 10, 14 and 20 all divide without a remainder — every other common multiple of the three is a multiple of it.

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

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

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

    Prime factor101420Highest power
    2222222
    55—55
    7—7—7

    LCM = 22 × 5 × 7 = 140

    Checking the LCM of 10, 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(10, 14) = (10 × 14) ÷ 2 = 140 ÷ 2 = 70

    LCM(70, 20) = (70 × 20) ÷ 10 = 1,400 ÷ 10 = 140

    LCM(10, 14, 20) = 140

    The pairs may be taken in any order — 14 and 20 first, then 10 — and the answer is the same 140. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 10, 14 and 20?. The LCM of 10, 14 and 20 is 140 — 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
    5101470
    61014210
    7101470
    81014280
    91014630
    10101470
    101114770
    101214420
    101314910
    10141470
    101415210
    101416560
    1014171,190
    101418630
    1014191,330
    101420140
    101421210
    101422770
    1014231,610
    101424840
    101425350
    101426910
    1014271,890
    101428140
    1014292,030
    101430210
    1014312,170
    1014321,120
    1014332,310
    1014341,190

    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, 14 and 20? (The answer is: 140). Enter the first number (e.g. '10'), 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 10, 14 and 20?

    LCM of 10, 14 and 20 is 140

    How to find the LCM of 10, 14 and 20 by prime factorization?

    Take every prime that appears in 10, 14 and 20 to the highest power it reaches in any one of them and multiply: 2² × 5 × 7 = 140.

    Can you get the LCM of 10, 14 and 20 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 10 and 14 is 70, and the LCM of 70 and 20 is 140 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 140 divisible by 10, 14 and 20?

    Yes, and by definition it is the smallest positive integer that is: 140 ÷ 10, 140 ÷ 14 and 140 ÷ 20 all come out whole. Any other common multiple of 10, 14 and 20 is a multiple of 140.

    See Also