LCM for 8, 14 and 21

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What's the Least Common Multiple (LCM) of 8, 14 and 21?

Answer

LCM of 8, 14 and 21 is
168

First common multiples: 168, 336, 504, …

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

8 = 23

14 = 2 × 7

21 = 3 × 7

Prime81421Highest power
2232—23
3——33
7—777

— = 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
6814168
781456
881456
8914504
81014280
81114616
81214168
81314728
8141456
81415840
81416112
81417952
81418504
814191,064
81420280
81421168
81422616
814231,288
81424168
814251,400
81426728
814271,512
8142856
814291,624
81430840
814311,736
81432224
814331,848
81434952
81435280

FAQ

What's the Least Common Multiple (LCM) of 8, 14 and 21?

LCM of 8, 14 and 21 is 168

How to find the LCM of 8, 14 and 21 by prime factorization?

Take every prime that appears in 8, 14 and 21 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

Can you get the LCM of 8, 14 and 21 two numbers at a time?

Yes. The LCM of 8 and 14 is 56, and the LCM of 56 and 21 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 8, 14 and 21?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 8, 168 ÷ 14 and 168 ÷ 21 all come out whole. Any other common multiple of 8, 14 and 21 is a multiple of 168.

See Also