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    LCM for 8, 19 and 23

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

    What's the Least Common Multiple (LCM) of 8, 19 and 23?

    Answer

    LCM of 8, 19 and 23 is
    3,496

    (Three thousand four hundred ninety-six)

    3,496 is the smallest positive integer that 8, 19 and 23 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 19 and 23 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 8: 2 × 2 × 2 (exponent form: 23)

    All Prime Factors of 19: 19 (exponent form: 19)

    All Prime Factors of 23: 23 (exponent form: 23)

    Prime factor81923Highest power
    223——23
    19—19—19
    23——2323

    LCM = 23 × 19 × 23 = 3,496

    Checking the LCM of 8, 19 and 23 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(8, 19) = (8 × 19) ÷ 1 = 152 ÷ 1 = 152

    LCM(152, 23) = (152 × 23) ÷ 1 = 3,496 ÷ 1 = 3,496

    LCM(8, 19, 23) = 3,496

    The pairs may be taken in any order — 19 and 23 first, then 8 — and the answer is the same 3,496. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 8, 19 and 23?. The LCM of 8, 19 and 23 is 3,496 — 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
    8819152
    89191,368
    81019760
    811191,672
    81219456
    813191,976
    814191,064
    815192,280
    81619304
    817192,584
    818191,368
    81919152
    81920760
    819213,192
    819221,672
    819233,496
    81924456
    819253,800
    819261,976
    819274,104
    819281,064
    819294,408
    819302,280
    819314,712
    81932608
    819335,016
    819342,584
    819355,320
    819361,368
    819375,624

    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 8, 19 and 23? (The answer is: 3,496). Enter the first number (e.g. '8'), the second (e.g. '19') and the third (e.g. '23'), 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 8, 19 and 23?

    LCM of 8, 19 and 23 is 3,496

    How to find the LCM of 8, 19 and 23 by prime factorization?

    Take every prime that appears in 8, 19 and 23 to the highest power it reaches in any one of them and multiply: 2³ × 19 × 23 = 3,496.

    Can you get the LCM of 8, 19 and 23 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 19 is 152, and the LCM of 152 and 23 is 3,496 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 3,496 divisible by 8, 19 and 23?

    Yes, and by definition it is the smallest positive integer that is: 3,496 ÷ 8, 3,496 ÷ 19 and 3,496 ÷ 23 all come out whole. Any other common multiple of 8, 19 and 23 is a multiple of 3,496.

    See Also