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    LCM for 8, 28 and 30

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

    What's the Least Common Multiple (LCM) of 8, 28 and 30?

    Answer

    LCM of 8, 28 and 30 is
    840

    (Eight hundred forty)

    840 is the smallest positive integer that 8, 28 and 30 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 28 and 30 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 8: 2 × 2 × 2 (exponent form: 23)

    All Prime Factors of 28: 2 × 2 × 7 (exponent form: 22 × 7)

    All Prime Factors of 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

    Prime factor82830Highest power
    22322223
    3——33
    5——55
    7—7—7

    LCM = 23 × 3 × 5 × 7 = 840

    Checking the LCM of 8, 28 and 30 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(8, 28) = (8 × 28) ÷ 4 = 224 ÷ 4 = 56

    LCM(56, 30) = (56 × 30) ÷ 2 = 1,680 ÷ 2 = 840

    LCM(8, 28, 30) = 840

    The pairs may be taken in any order — 28 and 30 first, then 8 — and the answer is the same 840. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 8, 28 and 30?. The LCM of 8, 28 and 30 is 840 — 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
    81528840
    81628112
    81728952
    81828504
    819281,064
    82028280
    82128168
    82228616
    823281,288
    82428168
    825281,400
    82628728
    827281,512
    8282856
    828291,624
    82830840
    828311,736
    82832224
    828331,848
    82834952
    82835280
    82836504
    828372,072
    828381,064
    828392,184
    82840280
    828412,296
    82842168
    828432,408
    82844616

    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 8, 28 and 30? (The answer is: 840). Enter the first number (e.g. '8'), the second (e.g. '28') and the third (e.g. '30'), 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 8, 28 and 30?

    LCM of 8, 28 and 30 is 840

    How to find the LCM of 8, 28 and 30 by prime factorization?

    Take every prime that appears in 8, 28 and 30 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 × 7 = 840.

    Can you get the LCM of 8, 28 and 30 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 28 is 56, and the LCM of 56 and 30 is 840 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 840 divisible by 8, 28 and 30?

    Yes, and by definition it is the smallest positive integer that is: 840 ÷ 8, 840 ÷ 28 and 840 ÷ 30 all come out whole. Any other common multiple of 8, 28 and 30 is a multiple of 840.

    See Also