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    LCM for 10, 20 and 30

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

    What's the Least Common Multiple (LCM) of 10, 20 and 30?

    Answer

    LCM of 10, 20 and 30 is
    60

    (Sixty)

    60 is the smallest positive integer that 10, 20 and 30 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 10, 20 and 30 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 20: 2 × 2 × 5 (exponent form: 22 × 5)

    All Prime Factors of 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

    Prime factor102030Highest power
    2222222
    3——33
    55555

    LCM = 22 × 3 × 5 = 60

    Checking the LCM of 10, 20 and 30 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, 20) = (10 × 20) ÷ 10 = 200 ÷ 10 = 20

    LCM(20, 30) = (20 × 30) ÷ 10 = 600 ÷ 10 = 60

    LCM(10, 20, 30) = 60

    The pairs may be taken in any order — 20 and 30 first, then 10 — and the answer is the same 60. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 10, 20 and 30?. The LCM of 10, 20 and 30 is 60 — 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
    10152060
    10162080
    101720340
    101820180
    101920380
    10202020
    102021420
    102022220
    102023460
    102024120
    102025100
    102026260
    102027540
    102028140
    102029580
    10203060
    102031620
    102032160
    102033660
    102034340
    102035140
    102036180
    102037740
    102038380
    102039780
    10204040
    102041820
    102042420
    102043860
    102044220

    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, 20 and 30? (The answer is: 60). Enter the first number (e.g. '10'), the second (e.g. '20') and the third (e.g. '30'), 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, 20 and 30?

    LCM of 10, 20 and 30 is 60

    How to find the LCM of 10, 20 and 30 by prime factorization?

    Take every prime that appears in 10, 20 and 30 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

    Can you get the LCM of 10, 20 and 30 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 10 and 20 is 20, and the LCM of 20 and 30 is 60 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 60 divisible by 10, 20 and 30?

    Yes, and by definition it is the smallest positive integer that is: 60 ÷ 10, 60 ÷ 20 and 60 ÷ 30 all come out whole. Any other common multiple of 10, 20 and 30 is a multiple of 60.

    See Also