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    LCM for 6, 21 and 45

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

    What's the Least Common Multiple (LCM) of 6, 21 and 45?

    Answer

    LCM of 6, 21 and 45 is
    630

    (Six hundred thirty)

    630 is the smallest positive integer that 6, 21 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 6, 21 and 45 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 21: 3 × 7 (exponent form: 3 × 7)

    All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

    Prime factor62145Highest power
    22——2
    3333232
    5——55
    7—7—7

    LCM = 2 × 32 × 5 × 7 = 630

    Checking the LCM of 6, 21 and 45 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, 21) = (6 × 21) ÷ 3 = 126 ÷ 3 = 42

    LCM(42, 45) = (42 × 45) ÷ 3 = 1,890 ÷ 3 = 630

    LCM(6, 21, 45) = 630

    The pairs may be taken in any order — 21 and 45 first, then 6 — and the answer is the same 630. 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, 21 and 45?. The LCM of 6, 21 and 45 is 630 — 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
    62130210
    621311,302
    62132672
    62133462
    62134714
    62135210
    62136252
    621371,554
    62138798
    62139546
    62140840
    621411,722
    6214242
    621431,806
    62144924
    62145630
    62146966
    621471,974
    62148336
    62149294
    621501,050
    62151714
    621521,092
    621532,226
    62154378
    621552,310
    62156168
    62157798
    621581,218
    621592,478

    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, 21 and 45? (The answer is: 630). Enter the first number (e.g. '6'), the second (e.g. '21') and the third (e.g. '45'), 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, 21 and 45?

    LCM of 6, 21 and 45 is 630

    How to find the LCM of 6, 21 and 45 by prime factorization?

    Take every prime that appears in 6, 21 and 45 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 × 7 = 630.

    Can you get the LCM of 6, 21 and 45 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 6 and 21 is 42, and the LCM of 42 and 45 is 630 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 630 divisible by 6, 21 and 45?

    Yes, and by definition it is the smallest positive integer that is: 630 ÷ 6, 630 ÷ 21 and 630 ÷ 45 all come out whole. Any other common multiple of 6, 21 and 45 is a multiple of 630.

    See Also