LCM for 6, 8 and 14

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What's the Least Common Multiple (LCM) of 6, 8 and 14?

Answer

LCM of 6, 8 and 14 is
168

First common multiples: 168, 336, 504, …

168 is divisible by all three: 168 ÷ 6 = 28, 168 ÷ 8 = 21, 168 ÷ 14 = 12 — and 28, 21 and 12 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 28 and of y/8 by 21 and of z/14 by 12.

6 = 2 × 3

8 = 23

14 = 2 × 7

Prime6814Highest power
2223223
33——3
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 × 7 = 168

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LCM Table

1st2nd3rdLCM
16824
26824
36824
46824
568120
66824
678168
68824
68972
6810120
6811264
681224
6813312
6814168
6815120
681648
6817408
681872
6819456
6820120
6821168
6822264
6823552
682424
6825600
6826312
6827216
6828168
6829696
6830120

FAQ

What's the Least Common Multiple (LCM) of 6, 8 and 14?

LCM of 6, 8 and 14 is 168

How to find the LCM of 6, 8 and 14 by prime factorization?

Take every prime that appears in 6, 8 and 14 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

Can you get the LCM of 6, 8 and 14 two numbers at a time?

Yes. The LCM of 6 and 8 is 24, and the LCM of 24 and 14 is 168 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 168 divisible by 6, 8 and 14?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 6, 168 ÷ 8 and 168 ÷ 14 all come out whole. Any other common multiple of 6, 8 and 14 is a multiple of 168.

See Also