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    LCM for 18, 24 and 42

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

    What's the Least Common Multiple (LCM) of 18, 24 and 42?

    Answer

    LCM of 18, 24 and 42 is
    504

    (Five hundred four)

    504 is the smallest positive integer that 18, 24 and 42 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 18, 24 and 42 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

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

    All Prime Factors of 42: 2 × 3 × 7 (exponent form: 2 × 3 × 7)

    Prime factor182442Highest power
    2223223
    3323332
    7——77

    LCM = 23 × 32 × 7 = 504

    Checking the LCM of 18, 24 and 42 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(18, 24) = (18 × 24) ÷ 6 = 432 ÷ 6 = 72

    LCM(72, 42) = (72 × 42) ÷ 6 = 3,024 ÷ 6 = 504

    LCM(18, 24, 42) = 504

    The pairs may be taken in any order — 24 and 42 first, then 18 — and the answer is the same 504. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 18, 24 and 42?. The LCM of 18, 24 and 42 is 504 — 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
    182427216
    182428504
    1824292,088
    182430360
    1824312,232
    182432288
    182433792
    1824341,224
    1824352,520
    18243672
    1824372,664
    1824381,368
    182439936
    182440360
    1824412,952
    182442504
    1824433,096
    182444792
    182445360
    1824461,656
    1824473,384
    182448144
    1824493,528
    1824501,800
    1824511,224
    182452936
    1824533,816
    182454216
    1824553,960
    182456504

    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 18, 24 and 42? (The answer is: 504). Enter the first number (e.g. '18'), the second (e.g. '24') and the third (e.g. '42'), 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 18, 24 and 42?

    LCM of 18, 24 and 42 is 504

    How to find the LCM of 18, 24 and 42 by prime factorization?

    Take every prime that appears in 18, 24 and 42 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 7 = 504.

    Can you get the LCM of 18, 24 and 42 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 18 and 24 is 72, and the LCM of 72 and 42 is 504 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 504 divisible by 18, 24 and 42?

    Yes, and by definition it is the smallest positive integer that is: 504 ÷ 18, 504 ÷ 24 and 504 ÷ 42 all come out whole. Any other common multiple of 18, 24 and 42 is a multiple of 504.

    See Also