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    LCM for 5, 14 and 20

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

    What's the Least Common Multiple (LCM) of 5, 14 and 20?

    Answer

    LCM of 5, 14 and 20 is
    140

    (One hundred forty)

    140 is the smallest positive integer that 5, 14 and 20 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 5, 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 5: 5 (exponent form: 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 factor51420Highest power
    2—22222
    55—55
    7—7—7

    LCM = 22 × 5 × 7 = 140

    Checking the LCM of 5, 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(5, 14) = (5 × 14) ÷ 1 = 70 ÷ 1 = 70

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

    LCM(5, 14, 20) = 140

    The pairs may be taken in any order — 14 and 20 first, then 5 — 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 5, 14 and 20?. The LCM of 5, 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
    551470
    5614210
    571470
    5814280
    5914630
    5101470
    51114770
    51214420
    51314910
    5141470
    51415210
    51416560
    514171,190
    51418630
    514191,330
    51420140
    51421210
    51422770
    514231,610
    51424840
    51425350
    51426910
    514271,890
    51428140
    514292,030
    51430210
    514312,170
    514321,120
    514332,310
    514341,190

    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 5, 14 and 20? (The answer is: 140). Enter the first number (e.g. '5'), 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 5, 14 and 20?

    LCM of 5, 14 and 20 is 140

    How to find the LCM of 5, 14 and 20 by prime factorization?

    Take every prime that appears in 5, 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 5, 14 and 20 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 5 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 5, 14 and 20?

    Yes, and by definition it is the smallest positive integer that is: 140 ÷ 5, 140 ÷ 14 and 140 ÷ 20 all come out whole. Any other common multiple of 5, 14 and 20 is a multiple of 140.

    See Also