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    LCM for 12, 18 and 30

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

    What's the Least Common Multiple (LCM) of 12, 18 and 30?

    Answer

    LCM of 12, 18 and 30 is
    180

    (One hundred eighty)

    180 is the smallest positive integer that 12, 18 and 30 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 12, 18 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 12: 2 × 2 × 3 (exponent form: 22 × 3)

    All Prime Factors of 18: 2 × 3 × 3 (exponent form: 2 × 32)

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

    Prime factor121830Highest power
    2222222
    3332332
    5——55

    LCM = 22 × 32 × 5 = 180

    Checking the LCM of 12, 18 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(12, 18) = (12 × 18) ÷ 6 = 216 ÷ 6 = 36

    LCM(36, 30) = (36 × 30) ÷ 6 = 1,080 ÷ 6 = 180

    LCM(12, 18, 30) = 180

    The pairs may be taken in any order — 18 and 30 first, then 12 — and the answer is the same 180. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 12, 18 and 30?. The LCM of 12, 18 and 30 is 180 — 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
    121518180
    121618144
    121718612
    12181836
    121819684
    121820180
    121821252
    121822396
    121823828
    12182472
    121825900
    121826468
    121827108
    121828252
    1218291,044
    121830180
    1218311,116
    121832288
    121833396
    121834612
    1218351,260
    12183636
    1218371,332
    121838684
    121839468
    121840360
    1218411,476
    121842252
    1218431,548
    121844396

    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 12, 18 and 30? (The answer is: 180). Enter the first number (e.g. '12'), the second (e.g. '18') 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 12, 18 and 30?

    LCM of 12, 18 and 30 is 180

    How to find the LCM of 12, 18 and 30 by prime factorization?

    Take every prime that appears in 12, 18 and 30 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

    Can you get the LCM of 12, 18 and 30 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 12 and 18 is 36, and the LCM of 36 and 30 is 180 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 180 divisible by 12, 18 and 30?

    Yes, and by definition it is the smallest positive integer that is: 180 ÷ 12, 180 ÷ 18 and 180 ÷ 30 all come out whole. Any other common multiple of 12, 18 and 30 is a multiple of 180.

    See Also