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    LCM for 5, 12 and 18

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

    What's the Least Common Multiple (LCM) of 5, 12 and 18?

    Answer

    LCM of 5, 12 and 18 is
    180

    (One hundred eighty)

    180 is the smallest positive integer that 5, 12 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 5, 12 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 5: 5 (exponent form: 5)

    All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

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

    Prime factor51218Highest power
    2—22222
    3—33232
    55——5

    LCM = 22 × 32 × 5 = 180

    Checking the LCM of 5, 12 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(5, 12) = (5 × 12) ÷ 1 = 60 ÷ 1 = 60

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

    LCM(5, 12, 18) = 180

    The pairs may be taken in any order — 12 and 18 first, then 5 — 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 5, 12 and 18?. The LCM of 5, 12 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
    351260
    451260
    551260
    561260
    5712420
    5812120
    5912180
    5101260
    51112660
    5121260
    51213780
    51214420
    5121560
    51216240
    512171,020
    51218180
    512191,140
    5122060
    51221420
    51222660
    512231,380
    51224120
    51225300
    51226780
    51227540
    51228420
    512291,740
    5123060
    512311,860
    51232480

    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, 12 and 18? (The answer is: 180). Enter the first number (e.g. '5'), the second (e.g. '12') 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 5, 12 and 18?

    LCM of 5, 12 and 18 is 180

    How to find the LCM of 5, 12 and 18 by prime factorization?

    Take every prime that appears in 5, 12 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 5, 12 and 18 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 5 and 12 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 5, 12 and 18?

    Yes, and by definition it is the smallest positive integer that is: 180 ÷ 5, 180 ÷ 12 and 180 ÷ 18 all come out whole. Any other common multiple of 5, 12 and 18 is a multiple of 180.

    See Also