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    LCM for 12, 15 and 60

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

    What's the Least Common Multiple (LCM) of 12, 15 and 60?

    Answer

    LCM of 12, 15 and 60 is
    60

    (Sixty)

    60 is the smallest positive integer that 12, 15 and 60 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 12, 15 and 60 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 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

    Prime factor121560Highest power
    222—2222
    33333
    5—555

    LCM = 22 × 3 × 5 = 60

    Checking the LCM of 12, 15 and 60 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, 60) = (60 × 60) ÷ 60 = 3,600 ÷ 60 = 60

    LCM(12, 15, 60) = 60

    The pairs may be taken in any order — 15 and 60 first, then 12 — 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 12, 15 and 60?. The LCM of 12, 15 and 60 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
    121545180
    1215461,380
    1215472,820
    121548240
    1215492,940
    121550300
    1215511,020
    121552780
    1215533,180
    121554540
    121555660
    121556840
    1215571,140
    1215581,740
    1215593,540
    12156060
    1215613,660
    1215621,860
    1215631,260
    121564960
    121565780
    121566660
    1215674,020
    1215681,020
    1215691,380
    121570420
    1215714,260
    121572360
    1215734,380
    1215742,220

    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 60? (The answer is: 60). Enter the first number (e.g. '12'), the second (e.g. '15') and the third (e.g. '60'), 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 60?

    LCM of 12, 15 and 60 is 60

    How to find the LCM of 12, 15 and 60 by prime factorization?

    Take every prime that appears in 12, 15 and 60 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

    Can you get the LCM of 12, 15 and 60 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 60 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 12, 15 and 60?

    Yes, and by definition it is the smallest positive integer that is: 60 ÷ 12, 60 ÷ 15 and 60 ÷ 60 all come out whole. Any other common multiple of 12, 15 and 60 is a multiple of 60.

    See Also