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    LCM for 16, 18 and 24

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

    What's the Least Common Multiple (LCM) of 16, 18 and 24?

    Answer

    LCM of 16, 18 and 24 is
    144

    (One hundred forty-four)

    144 is the smallest positive integer that 16, 18 and 24 all divide without a remainder — every other common multiple of the three is a multiple of it.

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

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

    All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    Prime factor161824Highest power
    22422324
    3—32332

    LCM = 24 × 32 = 144

    Checking the LCM of 16, 18 and 24 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(16, 18) = (16 × 18) ÷ 2 = 288 ÷ 2 = 144

    LCM(144, 24) = (144 × 24) ÷ 24 = 3,456 ÷ 24 = 144

    LCM(16, 18, 24) = 144

    The pairs may be taken in any order — 18 and 24 first, then 16 — and the answer is the same 144. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 16, 18 and 24?. The LCM of 16, 18 and 24 is 144 — 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
    91618144
    101618720
    1116181,584
    121618144
    1316181,872
    1416181,008
    151618720
    161618144
    1617182,448
    161818144
    1618192,736
    161820720
    1618211,008
    1618221,584
    1618233,312
    161824144
    1618253,600
    1618261,872
    161827432
    1618281,008
    1618294,176
    161830720
    1618314,464
    161832288
    1618331,584
    1618342,448
    1618355,040
    161836144
    1618375,328
    1618382,736

    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 16, 18 and 24? (The answer is: 144). Enter the first number (e.g. '16'), the second (e.g. '18') and the third (e.g. '24'), 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 16, 18 and 24?

    LCM of 16, 18 and 24 is 144

    How to find the LCM of 16, 18 and 24 by prime factorization?

    Take every prime that appears in 16, 18 and 24 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² = 144.

    Can you get the LCM of 16, 18 and 24 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 16 and 18 is 144, and the LCM of 144 and 24 is 144 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 144 divisible by 16, 18 and 24?

    Yes, and by definition it is the smallest positive integer that is: 144 ÷ 16, 144 ÷ 18 and 144 ÷ 24 all come out whole. Any other common multiple of 16, 18 and 24 is a multiple of 144.

    See Also