LCM for 6, 21 and 45

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Least Common Multiple of
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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

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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.

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