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    LCM for 8, 15 and 21

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

    What's the Least Common Multiple (LCM) of 8, 15 and 21?

    Answer

    LCM of 8, 15 and 21 is
    840

    (Eight hundred forty)

    840 is the smallest positive integer that 8, 15 and 21 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 15 and 21 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 15: 3 × 5 (exponent form: 3 × 5)

    All Prime Factors of 21: 3 × 7 (exponent form: 3 × 7)

    Prime factor81521Highest power
    223——23
    3—333
    5—5—5
    7——77

    LCM = 23 × 3 × 5 × 7 = 840

    Checking the LCM of 8, 15 and 21 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, 15) = (8 × 15) ÷ 1 = 120 ÷ 1 = 120

    LCM(120, 21) = (120 × 21) ÷ 3 = 2,520 ÷ 3 = 840

    LCM(8, 15, 21) = 840

    The pairs may be taken in any order — 15 and 21 first, then 8 — and the answer is the same 840. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 8, 15 and 21?. The LCM of 8, 15 and 21 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
    6815120
    7815840
    8815120
    8915360
    81015120
    811151,320
    81215120
    813151,560
    81415840
    81515120
    81516240
    815172,040
    81518360
    815192,280
    81520120
    81521840
    815221,320
    815232,760
    81524120
    81525600
    815261,560
    815271,080
    81528840
    815293,480
    81530120
    815313,720
    81532480
    815331,320
    815342,040
    81535840

    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, 15 and 21? (The answer is: 840). Enter the first number (e.g. '8'), the second (e.g. '15') and the third (e.g. '21'), 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, 15 and 21?

    LCM of 8, 15 and 21 is 840

    How to find the LCM of 8, 15 and 21 by prime factorization?

    Take every prime that appears in 8, 15 and 21 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, 15 and 21 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 15 is 120, and the LCM of 120 and 21 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, 15 and 21?

    Yes, and by definition it is the smallest positive integer that is: 840 ÷ 8, 840 ÷ 15 and 840 ÷ 21 all come out whole. Any other common multiple of 8, 15 and 21 is a multiple of 840.

    See Also