LCM for 14, 16 and 18

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What's the Least Common Multiple (LCM) of 14, 16 and 18?

Answer

LCM of 14, 16 and 18 is
1,008

First common multiples: 1,008; 2,016; 3,024; …

1,008 is divisible by all three: 1,008 ÷ 14 = 72; 1,008 ÷ 16 = 63; 1,008 ÷ 18 = 56 — and 72, 63 and 56 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/14 by 72 and of y/16 by 63 and of z/18 by 56.

14 = 2 × 7

16 = 24

18 = 2 × 32

Prime141618Highest power
2224224
3——3232
77——7

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

LCM = 24 × 32 × 7 = 1,008

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LCM Table

1st2nd3rdLCM
31416336
41416112
51416560
61416336
71416112
81416112
914161,008
101416560
1114161,232
121416336
1314161,456
141416112
1415161,680
141616112
1416171,904
1416181,008
1416192,128
141620560
141621336
1416221,232
1416232,576
141624336
1416252,800
1416261,456
1416273,024
141628112
1416293,248
1416301,680
1416313,472
141632224

FAQ

What's the Least Common Multiple (LCM) of 14, 16 and 18?

LCM of 14, 16 and 18 is 1,008

How to find the LCM of 14, 16 and 18 by prime factorization?

Take every prime that appears in 14, 16 and 18 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² × 7 = 1,008.

Can you get the LCM of 14, 16 and 18 two numbers at a time?

Yes. The LCM of 14 and 16 is 112, and the LCM of 112 and 18 is 1,008 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 1,008 divisible by 14, 16 and 18?

Yes, and by definition it is the smallest positive integer that is: 1,008 ÷ 14, 1,008 ÷ 16 and 1,008 ÷ 18 all come out whole. Any other common multiple of 14, 16 and 18 is a multiple of 1,008.

See Also