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    LCM for 6, 12 and 30

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

    What's the Least Common Multiple (LCM) of 6, 12 and 30?

    Answer

    LCM of 6, 12 and 30 is
    60

    (Sixty)

    60 is the smallest positive integer that 6, 12 and 30 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 6, 12 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 6: 2 × 3 (exponent form: 2 × 3)

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

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

    Prime factor61230Highest power
    2222222
    33333
    5——55

    LCM = 22 × 3 × 5 = 60

    Checking the LCM of 6, 12 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(6, 12) = (6 × 12) ÷ 6 = 72 ÷ 6 = 12

    LCM(12, 30) = (12 × 30) ÷ 6 = 360 ÷ 6 = 60

    LCM(6, 12, 30) = 60

    The pairs may be taken in any order — 12 and 30 first, then 6 — 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 6, 12 and 30?. The LCM of 6, 12 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
    6121560
    6121648
    61217204
    6121836
    61219228
    6122060
    6122184
    61222132
    61223276
    6122424
    61225300
    61226156
    61227108
    6122884
    61229348
    6123060
    61231372
    6123296
    61233132
    61234204
    61235420
    6123636
    61237444
    61238228
    61239156
    61240120
    61241492
    6124284
    61243516
    61244132

    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 6, 12 and 30? (The answer is: 60). Enter the first number (e.g. '6'), the second (e.g. '12') 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 6, 12 and 30?

    LCM of 6, 12 and 30 is 60

    How to find the LCM of 6, 12 and 30 by prime factorization?

    Take every prime that appears in 6, 12 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 6, 12 and 30 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 6 and 12 is 12, and the LCM of 12 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 6, 12 and 30?

    Yes, and by definition it is the smallest positive integer that is: 60 ÷ 6, 60 ÷ 12 and 60 ÷ 30 all come out whole. Any other common multiple of 6, 12 and 30 is a multiple of 60.

    See Also