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    LCM for 2, 5 and 12

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

    What's the Least Common Multiple (LCM) of 2, 5 and 12?

    Answer

    LCM of 2, 5 and 12 is
    60

    (Sixty)

    60 is the smallest positive integer that 2, 5 and 12 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 2, 5 and 12 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 2: 2 (exponent form: 2)

    All Prime Factors of 5: 5 (exponent form: 5)

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

    Prime factor2512Highest power
    22—2222
    3——33
    5—5—5

    LCM = 22 × 3 × 5 = 60

    Checking the LCM of 2, 5 and 12 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(2, 5) = (2 × 5) ÷ 1 = 10 ÷ 1 = 10

    LCM(10, 12) = (10 × 12) ÷ 2 = 120 ÷ 2 = 60

    LCM(2, 5, 12) = 60

    The pairs may be taken in any order — 5 and 12 first, then 2 — 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 2, 5 and 12?. The LCM of 2, 5 and 12 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
    12510
    22510
    23530
    24520
    25510
    25630
    25770
    25840
    25990
    251010
    2511110
    251260
    2513130
    251470
    251530
    251680
    2517170
    251890
    2519190
    252020
    2521210
    2522110
    2523230
    2524120
    252550
    2526130
    2527270
    2528140
    2529290
    253030

    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 2, 5 and 12? (The answer is: 60). Enter the first number (e.g. '2'), the second (e.g. '5') and the third (e.g. '12'), 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 2, 5 and 12?

    LCM of 2, 5 and 12 is 60

    How to find the LCM of 2, 5 and 12 by prime factorization?

    Take every prime that appears in 2, 5 and 12 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

    Can you get the LCM of 2, 5 and 12 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 2 and 5 is 10, and the LCM of 10 and 12 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 2, 5 and 12?

    Yes, and by definition it is the smallest positive integer that is: 60 ÷ 2, 60 ÷ 5 and 60 ÷ 12 all come out whole. Any other common multiple of 2, 5 and 12 is a multiple of 60.

    See Also