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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

    First common multiples: 630; 1,260; 1,890; …

    630 is divisible by all three: 630 ÷ 6 = 105, 630 ÷ 21 = 30, 630 ÷ 45 = 14 — and 105, 30 and 14 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/6 by 105 and of y/21 by 30 and of z/45 by 14.

    6 = 2 × 3

    21 = 3 × 7

    45 = 32 × 5

    Prime62145Highest power
    22——2
    3333232
    5——55
    7—7—7

    — = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

    LCM = 2 × 32 × 5 × 7 = 630

    More with these numbers

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    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/6--21--45Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/6--21--45">What is the LCM of 6, 21 and 45? - Calculatio</a>Copy
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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.
    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/6--21--45/generated.jpgCopy

    LCM Table

    1st2nd3rdLCM
    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

    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. 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