LCM for 8, 15 and 21

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

Answer

LCM of 8, 15 and 21 is
840

First common multiples: 840; 1,680; 2,520; …

840 is divisible by all three: 840 ÷ 8 = 105, 840 ÷ 15 = 56, 840 ÷ 21 = 40 — and 105, 56 and 40 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/8 by 105 and of y/15 by 56 and of z/21 by 40.

8 = 23

15 = 3 × 5

21 = 3 × 7

Prime81521Highest power
223——23
3—333
5—5—5
7——77

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

LCM = 23 × 3 × 5 × 7 = 840

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LCM Table

1st2nd3rdLCM
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

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. 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