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    LCM for 12, 22 and 40

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

    What's the Least Common Multiple (LCM) of 12, 22 and 40?

    Answer

    LCM of 12, 22 and 40 is
    1,320

    (One thousand three hundred twenty)

    1,320 is the smallest positive integer that 12, 22 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 12, 22 and 40 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 22: 2 × 11 (exponent form: 2 × 11)

    All Prime Factors of 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

    Prime factor122240Highest power
    22222323
    33——3
    5——55
    11—11—11

    LCM = 23 × 3 × 5 × 11 = 1,320

    Checking the LCM of 12, 22 and 40 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, 22) = (12 × 22) ÷ 2 = 264 ÷ 2 = 132

    LCM(132, 40) = (132 × 40) ÷ 4 = 5,280 ÷ 4 = 1,320

    LCM(12, 22, 40) = 1,320

    The pairs may be taken in any order — 22 and 40 first, then 12 — and the answer is the same 1,320. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 12, 22 and 40?. The LCM of 12, 22 and 40 is 1,320 — 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
    1222253,300
    1222261,716
    1222271,188
    122228924
    1222293,828
    122230660
    1222314,092
    1222321,056
    122233132
    1222342,244
    1222354,620
    122236396
    1222374,884
    1222382,508
    1222391,716
    1222401,320
    1222415,412
    122242924
    1222435,676
    122244132
    1222451,980
    1222463,036
    1222476,204
    122248528
    1222496,468
    1222503,300
    1222512,244
    1222521,716
    1222536,996
    1222541,188

    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, 22 and 40? (The answer is: 1,320). Enter the first number (e.g. '12'), the second (e.g. '22') and the third (e.g. '40'), 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, 22 and 40?

    LCM of 12, 22 and 40 is 1,320

    How to find the LCM of 12, 22 and 40 by prime factorization?

    Take every prime that appears in 12, 22 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 × 11 = 1,320.

    Can you get the LCM of 12, 22 and 40 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 12 and 22 is 132, and the LCM of 132 and 40 is 1,320 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 1,320 divisible by 12, 22 and 40?

    Yes, and by definition it is the smallest positive integer that is: 1,320 ÷ 12, 1,320 ÷ 22 and 1,320 ÷ 40 all come out whole. Any other common multiple of 12, 22 and 40 is a multiple of 1,320.

    See Also