Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    LCM for 7, 18 and 21

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

    What's the Least Common Multiple (LCM) of 7, 18 and 21?

    Answer

    LCM of 7, 18 and 21 is
    126

    (One hundred twenty-six)

    126 is the smallest positive integer that 7, 18 and 21 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 7, 18 and 21 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 7: 7 (exponent form: 7)

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

    All Prime Factors of 21: 3 × 7 (exponent form: 3 × 7)

    Prime factor71821Highest power
    2—2—2
    3—32332
    77—77

    LCM = 2 × 32 × 7 = 126

    Checking the LCM of 7, 18 and 21 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(7, 18) = (7 × 18) ÷ 1 = 126 ÷ 1 = 126

    LCM(126, 21) = (126 × 21) ÷ 21 = 2,646 ÷ 21 = 126

    LCM(7, 18, 21) = 126

    The pairs may be taken in any order — 18 and 21 first, then 7 — and the answer is the same 126. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/7--18--21Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/7--18--21">What is the LCM of 7, 18 and 21? - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    What is the LCM of 7, 18 and 21?. The LCM of 7, 18 and 21 is 126 — the smallest number all three divide with no remainder. Step-by-step solution for three numbers.
    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/7--18--21/generated.jpgCopy

    LCM Table

    Number 1Number 2Number 3LCM
    6718126
    7718126
    7818504
    7918126
    71018630
    711181,386
    71218252
    713181,638
    71418126
    71518630
    716181,008
    717182,142
    71818126
    718192,394
    718201,260
    71821126
    718221,386
    718232,898
    71824504
    718253,150
    718261,638
    71827378
    71828252
    718293,654
    71830630
    718313,906
    718322,016
    718331,386
    718342,142
    71835630

    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 7, 18 and 21? (The answer is: 126). Enter the first number (e.g. '7'), the second (e.g. '18') and the third (e.g. '21'), 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 7, 18 and 21?

    LCM of 7, 18 and 21 is 126

    How to find the LCM of 7, 18 and 21 by prime factorization?

    Take every prime that appears in 7, 18 and 21 to the highest power it reaches in any one of them and multiply: 2 × 3² × 7 = 126.

    Can you get the LCM of 7, 18 and 21 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 7 and 18 is 126, and the LCM of 126 and 21 is 126 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 126 divisible by 7, 18 and 21?

    Yes, and by definition it is the smallest positive integer that is: 126 ÷ 7, 126 ÷ 18 and 126 ÷ 21 all come out whole. Any other common multiple of 7, 18 and 21 is a multiple of 126.

    See Also