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 6, 7 and 10

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

    What's the Least Common Multiple (LCM) of 6, 7 and 10?

    Answer

    LCM of 6, 7 and 10 is
    210

    (Two hundred ten)

    210 is the smallest positive integer that 6, 7 and 10 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 6, 7 and 10 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 6: 2 × 3 (exponent form: 2 × 3)

    All Prime Factors of 7: 7 (exponent form: 7)

    All Prime Factors of 10: 2 × 5 (exponent form: 2 × 5)

    Prime factor6710Highest power
    22—22
    33——3
    5——55
    7—7—7

    LCM = 2 × 3 × 5 × 7 = 210

    Checking the LCM of 6, 7 and 10 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(6, 7) = (6 × 7) ÷ 1 = 42 ÷ 1 = 42

    LCM(42, 10) = (42 × 10) ÷ 2 = 420 ÷ 2 = 210

    LCM(6, 7, 10) = 210

    The pairs may be taken in any order — 7 and 10 first, then 6 — and the answer is the same 210. 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/6--7--10Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/6--7--10">What is the LCM of 6, 7 and 10? - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    What is the LCM of 6, 7 and 10?. The LCM of 6, 7 and 10 is 210 — 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/6--7--10/generated.jpgCopy

    LCM Table

    Number 1Number 2Number 3LCM
    16742
    26742
    36742
    46784
    567210
    66742
    67742
    678168
    679126
    6710210
    6711462
    671284
    6713546
    671442
    6715210
    6716336
    6717714
    6718126
    6719798
    6720420
    672142
    6722462
    6723966
    6724168
    67251,050
    6726546
    6727378
    672884
    67291,218
    6730210

    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 6, 7 and 10? (The answer is: 210). Enter the first number (e.g. '6'), the second (e.g. '7') and the third (e.g. '10'), 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 6, 7 and 10?

    LCM of 6, 7 and 10 is 210

    How to find the LCM of 6, 7 and 10 by prime factorization?

    Take every prime that appears in 6, 7 and 10 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5 × 7 = 210.

    Can you get the LCM of 6, 7 and 10 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 6 and 7 is 42, and the LCM of 42 and 10 is 210 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 210 divisible by 6, 7 and 10?

    Yes, and by definition it is the smallest positive integer that is: 210 ÷ 6, 210 ÷ 7 and 210 ÷ 10 all come out whole. Any other common multiple of 6, 7 and 10 is a multiple of 210.

    See Also