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    LCM for 10, 16 and 18

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

    What's the Least Common Multiple (LCM) of 10, 16 and 18?

    Answer

    LCM of 10, 16 and 18 is
    720

    (Seven hundred twenty)

    720 is the smallest positive integer that 10, 16 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 10, 16 and 18 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

    All Prime Factors of 18: 2 × 3 × 3 (exponent form: 2 × 32)

    Prime factor101618Highest power
    2224224
    3——3232
    55——5

    LCM = 24 × 32 × 5 = 720

    Checking the LCM of 10, 16 and 18 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, 16) = (10 × 16) ÷ 2 = 160 ÷ 2 = 80

    LCM(80, 18) = (80 × 18) ÷ 2 = 1,440 ÷ 2 = 720

    LCM(10, 16, 18) = 720

    The pairs may be taken in any order — 16 and 18 first, then 10 — and the answer is the same 720. That is exactly why the two routes on this page agree.

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    What is the LCM of 10, 16 and 18?. The LCM of 10, 16 and 18 is 720 — 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
    31016240
    4101680
    5101680
    61016240
    71016560
    8101680
    91016720
    10101680
    101116880
    101216240
    1013161,040
    101416560
    101516240
    10161680
    1016171,360
    101618720
    1016191,520
    10162080
    1016211,680
    101622880
    1016231,840
    101624240
    101625400
    1016261,040
    1016272,160
    101628560
    1016292,320
    101630240
    1016312,480
    101632160

    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, 16 and 18? (The answer is: 720). Enter the first number (e.g. '10'), the second (e.g. '16') and the third (e.g. '18'), 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, 16 and 18?

    LCM of 10, 16 and 18 is 720

    How to find the LCM of 10, 16 and 18 by prime factorization?

    Take every prime that appears in 10, 16 and 18 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² × 5 = 720.

    Can you get the LCM of 10, 16 and 18 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 10 and 16 is 80, and the LCM of 80 and 18 is 720 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 720 divisible by 10, 16 and 18?

    Yes, and by definition it is the smallest positive integer that is: 720 ÷ 10, 720 ÷ 16 and 720 ÷ 18 all come out whole. Any other common multiple of 10, 16 and 18 is a multiple of 720.

    See Also