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    LCM for 18, 30 and 42

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

    What's the Least Common Multiple (LCM) of 18, 30 and 42?

    Answer

    LCM of 18, 30 and 42 is
    630

    (Six hundred thirty)

    630 is the smallest positive integer that 18, 30 and 42 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 18, 30 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 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

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

    Prime factor183042Highest power
    22222
    3323332
    5—5—5
    7——77

    LCM = 2 × 32 × 5 × 7 = 630

    Checking the LCM of 18, 30 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, 30) = (18 × 30) ÷ 6 = 540 ÷ 6 = 90

    LCM(90, 42) = (90 × 42) ÷ 6 = 3,780 ÷ 6 = 630

    LCM(18, 30, 42) = 630

    The pairs may be taken in any order — 30 and 42 first, then 18 — and the answer is the same 630. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 18, 30 and 42?. The LCM of 18, 30 and 42 is 630 — 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
    182730270
    1828301,260
    1829302,610
    18303090
    1830312,790
    1830321,440
    183033990
    1830341,530
    183035630
    183036180
    1830373,330
    1830381,710
    1830391,170
    183040360
    1830413,690
    183042630
    1830433,870
    1830441,980
    18304590
    1830462,070
    1830474,230
    183048720
    1830494,410
    183050450
    1830511,530
    1830522,340
    1830534,770
    183054270
    183055990
    1830562,520

    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, 30 and 42? (The answer is: 630). Enter the first number (e.g. '18'), the second (e.g. '30') 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, 30 and 42?

    LCM of 18, 30 and 42 is 630

    How to find the LCM of 18, 30 and 42 by prime factorization?

    Take every prime that appears in 18, 30 and 42 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 × 7 = 630.

    Can you get the LCM of 18, 30 and 42 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 18 and 30 is 90, and the LCM of 90 and 42 is 630 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 630 divisible by 18, 30 and 42?

    Yes, and by definition it is the smallest positive integer that is: 630 ÷ 18, 630 ÷ 30 and 630 ÷ 42 all come out whole. Any other common multiple of 18, 30 and 42 is a multiple of 630.

    See Also