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    LCM for 6, 8 and 36

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

    What's the Least Common Multiple (LCM) of 6, 8 and 36?

    Answer

    LCM of 6, 8 and 36 is
    72

    (Seventy-two)

    72 is the smallest positive integer that 6, 8 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 6, 8 and 36 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 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

    Prime factor6836Highest power
    22232223
    33—3232

    LCM = 23 × 32 = 72

    Checking the LCM of 6, 8 and 36 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, 36) = (24 × 36) ÷ 12 = 864 ÷ 12 = 72

    LCM(6, 8, 36) = 72

    The pairs may be taken in any order — 8 and 36 first, then 6 — and the answer is the same 72. 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 36?. The LCM of 6, 8 and 36 is 72 — 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
    6821168
    6822264
    6823552
    682424
    6825600
    6826312
    6827216
    6828168
    6829696
    6830120
    6831744
    683296
    6833264
    6834408
    6835840
    683672
    6837888
    6838456
    6839312
    6840120
    6841984
    6842168
    68431,032
    6844264
    6845360
    6846552
    68471,128
    684848
    68491,176
    6850600

    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 36? (The answer is: 72). Enter the first number (e.g. '6'), the second (e.g. '8') and the third (e.g. '36'), 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 36?

    LCM of 6, 8 and 36 is 72

    How to find the LCM of 6, 8 and 36 by prime factorization?

    Take every prime that appears in 6, 8 and 36 to the highest power it reaches in any one of them and multiply: 2³ × 3² = 72.

    Can you get the LCM of 6, 8 and 36 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 36 is 72 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 72 divisible by 6, 8 and 36?

    Yes, and by definition it is the smallest positive integer that is: 72 ÷ 6, 72 ÷ 8 and 72 ÷ 36 all come out whole. Any other common multiple of 6, 8 and 36 is a multiple of 72.

    See Also