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    LCM for 12, 15 and 40

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

    What's the Least Common Multiple (LCM) of 12, 15 and 40?

    Answer

    LCM of 12, 15 and 40 is
    120

    (One hundred twenty)

    120 is the smallest positive integer that 12, 15 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 12, 15 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 15: 3 × 5 (exponent form: 3 × 5)

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

    Prime factor121540Highest power
    222—2323
    333—3
    5—555

    LCM = 23 × 3 × 5 = 120

    Checking the LCM of 12, 15 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, 15) = (12 × 15) ÷ 3 = 180 ÷ 3 = 60

    LCM(60, 40) = (60 × 40) ÷ 20 = 2,400 ÷ 20 = 120

    LCM(12, 15, 40) = 120

    The pairs may be taken in any order — 15 and 40 first, then 12 — and the answer is the same 120. 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 40?. The LCM of 12, 15 and 40 is 120 — 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
    121525300
    121526780
    121527540
    121528420
    1215291,740
    12153060
    1215311,860
    121532480
    121533660
    1215341,020
    121535420
    121536180
    1215372,220
    1215381,140
    121539780
    121540120
    1215412,460
    121542420
    1215432,580
    121544660
    121545180
    1215461,380
    1215472,820
    121548240
    1215492,940
    121550300
    1215511,020
    121552780
    1215533,180
    121554540

    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 40? (The answer is: 120). Enter the first number (e.g. '12'), the second (e.g. '15') 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, 15 and 40?

    LCM of 12, 15 and 40 is 120

    How to find the LCM of 12, 15 and 40 by prime factorization?

    Take every prime that appears in 12, 15 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

    Can you get the LCM of 12, 15 and 40 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 40 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 120 divisible by 12, 15 and 40?

    Yes, and by definition it is the smallest positive integer that is: 120 ÷ 12, 120 ÷ 15 and 120 ÷ 40 all come out whole. Any other common multiple of 12, 15 and 40 is a multiple of 120.

    See Also