LCM for 8, 19 and 23

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What's the Least Common Multiple (LCM) of 8, 19 and 23?

Answer

LCM of 8, 19 and 23 is
3,496

First common multiples: 3,496; 6,992; 10,488; …

3,496 is divisible by all three: 3,496 ÷ 8 = 437; 3,496 ÷ 19 = 184; 3,496 ÷ 23 = 152 — and 437, 184 and 152 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 437 and of y/19 by 184 and of z/23 by 152.

8 = 23

19 — prime

23 — prime

Prime81923Highest power
223——23
19—19—19
23——2323

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

LCM = 23 × 19 × 23 = 3,496

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LCM Table

1st2nd3rdLCM
8819152
89191,368
81019760
811191,672
81219456
813191,976
814191,064
815192,280
81619304
817192,584
818191,368
81919152
81920760
819213,192
819221,672
819233,496
81924456
819253,800
819261,976
819274,104
819281,064
819294,408
819302,280
819314,712
81932608
819335,016
819342,584
819355,320
819361,368
819375,624

FAQ

What's the Least Common Multiple (LCM) of 8, 19 and 23?

LCM of 8, 19 and 23 is 3,496

How to find the LCM of 8, 19 and 23 by prime factorization?

Take every prime that appears in 8, 19 and 23 to the highest power it reaches in any one of them and multiply: 2³ × 19 × 23 = 3,496.

Can you get the LCM of 8, 19 and 23 two numbers at a time?

Yes. The LCM of 8 and 19 is 152, and the LCM of 152 and 23 is 3,496 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 3,496 divisible by 8, 19 and 23?

Yes, and by definition it is the smallest positive integer that is: 3,496 ÷ 8, 3,496 ÷ 19 and 3,496 ÷ 23 all come out whole. Any other common multiple of 8, 19 and 23 is a multiple of 3,496.

See Also