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    LCM for 12, 15 and 18

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

    What's the Least Common Multiple (LCM) of 12, 15 and 18?

    Answer

    LCM of 12, 15 and 18 is
    180

    (One hundred eighty)

    180 is the smallest positive integer that 12, 15 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 12, 15 and 18 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 15: 3 × 5 (exponent form: 3 × 5)

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

    Prime factor121518Highest power
    222—222
    3333232
    5—5—5

    LCM = 22 × 32 × 5 = 180

    Checking the LCM of 12, 15 and 18 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, 15) = (12 × 15) ÷ 3 = 180 ÷ 3 = 60

    LCM(60, 18) = (60 × 18) ÷ 6 = 1,080 ÷ 6 = 180

    LCM(12, 15, 18) = 180

    The pairs may be taken in any order — 15 and 18 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, 15 and 18?. The LCM of 12, 15 and 18 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
    3121560
    4121560
    5121560
    6121560
    71215420
    81215120
    91215180
    10121560
    111215660
    12121560
    121315780
    121415420
    12151560
    121516240
    1215171,020
    121518180
    1215191,140
    12152060
    121521420
    121522660
    1215231,380
    121524120
    121525300
    121526780
    121527540
    121528420
    1215291,740
    12153060
    1215311,860
    121532480

    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, 15 and 18? (The answer is: 180). Enter the first number (e.g. '12'), the second (e.g. '15') and the third (e.g. '18'), 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, 15 and 18?

    LCM of 12, 15 and 18 is 180

    How to find the LCM of 12, 15 and 18 by prime factorization?

    Take every prime that appears in 12, 15 and 18 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

    Can you get the LCM of 12, 15 and 18 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 12 and 15 is 60, and the LCM of 60 and 18 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, 15 and 18?

    Yes, and by definition it is the smallest positive integer that is: 180 ÷ 12, 180 ÷ 15 and 180 ÷ 18 all come out whole. Any other common multiple of 12, 15 and 18 is a multiple of 180.

    See Also