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    LCM for 3, 4 and 9

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

    What's the Least Common Multiple (LCM) of 3, 4 and 9?

    Answer

    LCM of 3, 4 and 9 is
    36

    (Thirty-six)

    36 is the smallest positive integer that 3, 4 and 9 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 3, 4 and 9 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 3: 3 (exponent form: 3)

    All Prime Factors of 4: 2 × 2 (exponent form: 22)

    All Prime Factors of 9: 3 × 3 (exponent form: 32)

    Prime factor349Highest power
    2—22—22
    33—3232

    LCM = 22 × 32 = 36

    Checking the LCM of 3, 4 and 9 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(3, 4) = (3 × 4) ÷ 1 = 12 ÷ 1 = 12

    LCM(12, 9) = (12 × 9) ÷ 3 = 108 ÷ 3 = 36

    LCM(3, 4, 9) = 36

    The pairs may be taken in any order — 4 and 9 first, then 3 — and the answer is the same 36. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 3, 4 and 9?. The LCM of 3, 4 and 9 is 36 — 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
    13412
    23412
    33412
    34412
    34560
    34612
    34784
    34824
    34936
    341060
    3411132
    341212
    3413156
    341484
    341560
    341648
    3417204
    341836
    3419228
    342060
    342184
    3422132
    3423276
    342424
    3425300
    3426156
    3427108
    342884
    3429348
    343060

    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 3, 4 and 9? (The answer is: 36). Enter the first number (e.g. '3'), the second (e.g. '4') and the third (e.g. '9'), 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 3, 4 and 9?

    LCM of 3, 4 and 9 is 36

    How to find the LCM of 3, 4 and 9 by prime factorization?

    Take every prime that appears in 3, 4 and 9 to the highest power it reaches in any one of them and multiply: 2² × 3² = 36.

    Can you get the LCM of 3, 4 and 9 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 3 and 4 is 12, and the LCM of 12 and 9 is 36 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 36 divisible by 3, 4 and 9?

    Yes, and by definition it is the smallest positive integer that is: 36 ÷ 3, 36 ÷ 4 and 36 ÷ 9 all come out whole. Any other common multiple of 3, 4 and 9 is a multiple of 36.

    See Also