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    LCM for 3, 8 and 10

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

    What's the Least Common Multiple (LCM) of 3, 8 and 10?

    Answer

    LCM of 3, 8 and 10 is
    120

    (One hundred twenty)

    120 is the smallest positive integer that 3, 8 and 10 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 3, 8 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 3: 3 (exponent form: 3)

    All Prime Factors of 8: 2 × 2 × 2 (exponent form: 23)

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

    Prime factor3810Highest power
    2—23223
    33——3
    5——55

    LCM = 23 × 3 × 5 = 120

    Checking the LCM of 3, 8 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(3, 8) = (3 × 8) ÷ 1 = 24 ÷ 1 = 24

    LCM(24, 10) = (24 × 10) ÷ 2 = 240 ÷ 2 = 120

    LCM(3, 8, 10) = 120

    The pairs may be taken in any order — 8 and 10 first, then 3 — and the answer is the same 120. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 3, 8 and 10?. The LCM of 3, 8 and 10 is 120 — 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
    13824
    23824
    33824
    34824
    358120
    36824
    378168
    38824
    38972
    3810120
    3811264
    381224
    3813312
    3814168
    3815120
    381648
    3817408
    381872
    3819456
    3820120
    3821168
    3822264
    3823552
    382424
    3825600
    3826312
    3827216
    3828168
    3829696
    3830120

    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, 8 and 10? (The answer is: 120). Enter the first number (e.g. '3'), the second (e.g. '8') 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 3, 8 and 10?

    LCM of 3, 8 and 10 is 120

    How to find the LCM of 3, 8 and 10 by prime factorization?

    Take every prime that appears in 3, 8 and 10 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

    Can you get the LCM of 3, 8 and 10 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 3 and 8 is 24, and the LCM of 24 and 10 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 120 divisible by 3, 8 and 10?

    Yes, and by definition it is the smallest positive integer that is: 120 ÷ 3, 120 ÷ 8 and 120 ÷ 10 all come out whole. Any other common multiple of 3, 8 and 10 is a multiple of 120.

    See Also