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    LCM for 12, 28 and 36

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

    What's the Least Common Multiple (LCM) of 12, 28 and 36?

    Answer

    LCM of 12, 28 and 36 is
    252

    (Two hundred fifty-two)

    252 is the smallest positive integer that 12, 28 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 12, 28 and 36 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 28: 2 × 2 × 7 (exponent form: 22 × 7)

    All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

    Prime factor122836Highest power
    222222222
    33—3232
    7—7—7

    LCM = 22 × 32 × 7 = 252

    Checking the LCM of 12, 28 and 36 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, 28) = (12 × 28) ÷ 4 = 336 ÷ 4 = 84

    LCM(84, 36) = (84 × 36) ÷ 12 = 3,024 ÷ 12 = 252

    LCM(12, 28, 36) = 252

    The pairs may be taken in any order — 28 and 36 first, then 12 — and the answer is the same 252. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 12, 28 and 36?. The LCM of 12, 28 and 36 is 252 — 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
    12212884
    122228924
    1223281,932
    122428168
    1225282,100
    1226281,092
    122728756
    12282884
    1228292,436
    122830420
    1228312,604
    122832672
    122833924
    1228341,428
    122835420
    122836252
    1228373,108
    1228381,596
    1228391,092
    122840840
    1228413,444
    12284284
    1228433,612
    122844924
    1228451,260
    1228461,932
    1228473,948
    122848336
    122849588
    1228502,100

    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, 28 and 36? (The answer is: 252). Enter the first number (e.g. '12'), the second (e.g. '28') and the third (e.g. '36'), 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, 28 and 36?

    LCM of 12, 28 and 36 is 252

    How to find the LCM of 12, 28 and 36 by prime factorization?

    Take every prime that appears in 12, 28 and 36 to the highest power it reaches in any one of them and multiply: 2² × 3² × 7 = 252.

    Can you get the LCM of 12, 28 and 36 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 12 and 28 is 84, and the LCM of 84 and 36 is 252 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 252 divisible by 12, 28 and 36?

    Yes, and by definition it is the smallest positive integer that is: 252 ÷ 12, 252 ÷ 28 and 252 ÷ 36 all come out whole. Any other common multiple of 12, 28 and 36 is a multiple of 252.

    See Also