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    LCM for 4, 10 and 20

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

    What's the Least Common Multiple (LCM) of 4, 10 and 20?

    Answer

    LCM of 4, 10 and 20 is
    20

    (Twenty)

    20 is the smallest positive integer that 4, 10 and 20 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 4, 10 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 4: 2 × 2 (exponent form: 22)

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

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

    Prime factor41020Highest power
    22222222
    5—555

    LCM = 22 × 5 = 20

    Checking the LCM of 4, 10 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(4, 10) = (4 × 10) ÷ 2 = 40 ÷ 2 = 20

    LCM(20, 20) = (20 × 20) ÷ 20 = 400 ÷ 20 = 20

    LCM(4, 10, 20) = 20

    The pairs may be taken in any order — 10 and 20 first, then 4 — and the answer is the same 20. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 4, 10 and 20?. The LCM of 4, 10 and 20 is 20 — 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
    451020
    461060
    4710140
    481040
    4910180
    4101020
    41011220
    4101260
    41013260
    41014140
    4101560
    4101680
    41017340
    41018180
    41019380
    4102020
    41021420
    41022220
    41023460
    41024120
    41025100
    41026260
    41027540
    41028140
    41029580
    4103060
    41031620
    41032160
    41033660
    41034340

    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 4, 10 and 20? (The answer is: 20). Enter the first number (e.g. '4'), the second (e.g. '10') 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 4, 10 and 20?

    LCM of 4, 10 and 20 is 20

    How to find the LCM of 4, 10 and 20 by prime factorization?

    Take every prime that appears in 4, 10 and 20 to the highest power it reaches in any one of them and multiply: 2² × 5 = 20.

    Can you get the LCM of 4, 10 and 20 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 4 and 10 is 20, and the LCM of 20 and 20 is 20 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 20 divisible by 4, 10 and 20?

    Yes, and by definition it is the smallest positive integer that is: 20 ÷ 4, 20 ÷ 10 and 20 ÷ 20 all come out whole. Any other common multiple of 4, 10 and 20 is a multiple of 20.

    See Also