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    LCM for 6, 8 and 22

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

    What's the Least Common Multiple (LCM) of 6, 8 and 22?

    Answer

    LCM of 6, 8 and 22 is
    264

    (Two hundred sixty-four)

    264 is the smallest positive integer that 6, 8 and 22 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 6, 8 and 22 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 8: 2 × 2 × 2 (exponent form: 23)

    All Prime Factors of 22: 2 × 11 (exponent form: 2 × 11)

    Prime factor6822Highest power
    2223223
    33——3
    11——1111

    LCM = 23 × 3 × 11 = 264

    Checking the LCM of 6, 8 and 22 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, 8) = (6 × 8) ÷ 2 = 48 ÷ 2 = 24

    LCM(24, 22) = (24 × 22) ÷ 2 = 528 ÷ 2 = 264

    LCM(6, 8, 22) = 264

    The pairs may be taken in any order — 8 and 22 first, then 6 — and the answer is the same 264. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 6, 8 and 22?. The LCM of 6, 8 and 22 is 264 — 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
    678168
    68824
    68972
    6810120
    6811264
    681224
    6813312
    6814168
    6815120
    681648
    6817408
    681872
    6819456
    6820120
    6821168
    6822264
    6823552
    682424
    6825600
    6826312
    6827216
    6828168
    6829696
    6830120
    6831744
    683296
    6833264
    6834408
    6835840
    683672

    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, 8 and 22? (The answer is: 264). Enter the first number (e.g. '6'), the second (e.g. '8') and the third (e.g. '22'), 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, 8 and 22?

    LCM of 6, 8 and 22 is 264

    How to find the LCM of 6, 8 and 22 by prime factorization?

    Take every prime that appears in 6, 8 and 22 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 11 = 264.

    Can you get the LCM of 6, 8 and 22 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 6 and 8 is 24, and the LCM of 24 and 22 is 264 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 264 divisible by 6, 8 and 22?

    Yes, and by definition it is the smallest positive integer that is: 264 ÷ 6, 264 ÷ 8 and 264 ÷ 22 all come out whole. Any other common multiple of 6, 8 and 22 is a multiple of 264.

    See Also