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    LCM for 12, 15 and 20

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

    What's the Least Common Multiple (LCM) of 12, 15 and 20?

    Answer

    LCM of 12, 15 and 20 is
    60

    (Sixty)

    60 is the smallest positive integer that 12, 15 and 20 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 12, 15 and 20 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 20: 2 × 2 × 5 (exponent form: 22 × 5)

    Prime factor121520Highest power
    222—2222
    333—3
    5—555

    LCM = 22 × 3 × 5 = 60

    Checking the LCM of 12, 15 and 20 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, 20) = (60 × 20) ÷ 20 = 1,200 ÷ 20 = 60

    LCM(12, 15, 20) = 60

    The pairs may be taken in any order — 15 and 20 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 20?. The LCM of 12, 15 and 20 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
    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
    121533660
    1215341,020

    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 20? (The answer is: 60). Enter the first number (e.g. '12'), the second (e.g. '15') and the third (e.g. '20'), 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 20?

    LCM of 12, 15 and 20 is 60

    How to find the LCM of 12, 15 and 20 by prime factorization?

    Take every prime that appears in 12, 15 and 20 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 20 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 20 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 20?

    Yes, and by definition it is the smallest positive integer that is: 60 ÷ 12, 60 ÷ 15 and 60 ÷ 20 all come out whole. Any other common multiple of 12, 15 and 20 is a multiple of 60.

    See Also