LCM for 14, 16 and 18

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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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

(One thousand eight)

1,008 is the smallest positive integer that 14, 16 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 14, 16 and 18 by Prime Factorization

Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

All Prime Factors of 14: 2 × 7 (exponent form: 2 × 7)

All Prime Factors of 16: 2 × 2 × 2 × 2 (exponent form: 24)

All Prime Factors of 18: 2 × 3 × 3 (exponent form: 2 × 32)

Prime factor141618Highest power
2224224
3——3232
77——7

LCM = 24 × 32 × 7 = 1,008

Checking the LCM of 14, 16 and 18 Two Numbers at a Time

The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

LCM(a, b) = (a × b) ÷ GCD(a, b)

LCM(14, 16) = (14 × 16) ÷ 2 = 224 ÷ 2 = 112

LCM(112, 18) = (112 × 18) ÷ 2 = 2,016 ÷ 2 = 1,008

LCM(14, 16, 18) = 1,008

The pairs may be taken in any order — 16 and 18 first, then 14 — and the answer is the same 1,008. That is exactly why the two routes on this page agree.

Related Calculations

See Also

About "Least Common Multiple of 3 Numbers" Calculator

This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 14, 16 and 18? (The answer is: 1,008). Enter the first number (e.g. '14'), the second (e.g. '16') and the third (e.g. '18'), then hit the 'Calculate' button.
The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

LCM Table

Number 1Number 2Number 3LCM
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, and it is the check this page prints. 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