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 10, 11 and 12

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

    What's the Least Common Multiple (LCM) of 10, 11 and 12?

    Answer

    LCM of 10, 11 and 12 is
    660

    (Six hundred sixty)

    660 is the smallest positive integer that 10, 11 and 12 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 10, 11 and 12 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 10: 2 × 5 (exponent form: 2 × 5)

    All Prime Factors of 11: 11 (exponent form: 11)

    All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

    Prime factor101112Highest power
    22—2222
    3——33
    55——5
    11—11—11

    LCM = 22 × 3 × 5 × 11 = 660

    Checking the LCM of 10, 11 and 12 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(10, 11) = (10 × 11) ÷ 1 = 110 ÷ 1 = 110

    LCM(110, 12) = (110 × 12) ÷ 2 = 1,320 ÷ 2 = 660

    LCM(10, 11, 12) = 660

    The pairs may be taken in any order — 11 and 12 first, then 10 — and the answer is the same 660. 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/10--11--12Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/10--11--12">What is the LCM of 10, 11 and 12? - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    What is the LCM of 10, 11 and 12?. The LCM of 10, 11 and 12 is 660 — 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/10--11--12/generated.jpgCopy

    LCM Table

    Number 1Number 2Number 3LCM
    11011110
    21011110
    31011330
    41011220
    51011110
    61011330
    71011770
    81011440
    91011990
    101011110
    101111110
    101112660
    1011131,430
    101114770
    101115330
    101116880
    1011171,870
    101118990
    1011192,090
    101120220
    1011212,310
    101122110
    1011232,530
    1011241,320
    101125550
    1011261,430
    1011272,970
    1011281,540
    1011293,190
    101130330

    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 10, 11 and 12? (The answer is: 660). Enter the first number (e.g. '10'), the second (e.g. '11') and the third (e.g. '12'), 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 10, 11 and 12?

    LCM of 10, 11 and 12 is 660

    How to find the LCM of 10, 11 and 12 by prime factorization?

    Take every prime that appears in 10, 11 and 12 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 11 = 660.

    Can you get the LCM of 10, 11 and 12 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 10 and 11 is 110, and the LCM of 110 and 12 is 660 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 660 divisible by 10, 11 and 12?

    Yes, and by definition it is the smallest positive integer that is: 660 ÷ 10, 660 ÷ 11 and 660 ÷ 12 all come out whole. Any other common multiple of 10, 11 and 12 is a multiple of 660.

    See Also