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    LCM for 10, 12 and 40

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

    What's the Least Common Multiple (LCM) of 10, 12 and 40?

    Answer

    LCM of 10, 12 and 40 is
    120

    (One hundred twenty)

    120 is the smallest positive integer that 10, 12 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 10, 12 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 10: 2 × 5 (exponent form: 2 × 5)

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

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

    Prime factor101240Highest power
    22222323
    3—3—3
    55—55

    LCM = 23 × 3 × 5 = 120

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

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

    LCM(10, 12, 40) = 120

    The pairs may be taken in any order — 12 and 40 first, then 10 — and the answer is the same 120. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 10, 12 and 40?. The LCM of 10, 12 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
    101225300
    101226780
    101227540
    101228420
    1012291,740
    10123060
    1012311,860
    101232480
    101233660
    1012341,020
    101235420
    101236180
    1012372,220
    1012381,140
    101239780
    101240120
    1012412,460
    101242420
    1012432,580
    101244660
    101245180
    1012461,380
    1012472,820
    101248240
    1012492,940
    101250300
    1012511,020
    101252780
    1012533,180
    101254540

    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 10, 12 and 40? (The answer is: 120). Enter the first number (e.g. '10'), the second (e.g. '12') 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 10, 12 and 40?

    LCM of 10, 12 and 40 is 120

    How to find the LCM of 10, 12 and 40 by prime factorization?

    Take every prime that appears in 10, 12 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 10, 12 and 40 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 10 and 12 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 10, 12 and 40?

    Yes, and by definition it is the smallest positive integer that is: 120 ÷ 10, 120 ÷ 12 and 120 ÷ 40 all come out whole. Any other common multiple of 10, 12 and 40 is a multiple of 120.

    See Also