LCM for 12, 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 12, 16 and 18?

Answer

LCM of 12, 16 and 18 is
144

(One hundred forty-four)

144 is the smallest positive integer that 12, 16 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 12, 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 12: 2 × 2 × 3 (exponent form: 22 × 3)

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 factor121618Highest power
22224224
33—3232

LCM = 24 × 32 = 144

Checking the LCM of 12, 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(12, 16) = (12 × 16) ÷ 4 = 192 ÷ 4 = 48

LCM(48, 18) = (48 × 18) ÷ 6 = 864 ÷ 6 = 144

LCM(12, 16, 18) = 144

The pairs may be taken in any order — 16 and 18 first, then 12 — and the answer is the same 144. That is exactly why the two routes on this page agree.

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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 12, 16 and 18? (The answer is: 144). Enter the first number (e.g. '12'), 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
3121648
4121648
51216240
6121648
71216336
8121648
91216144
101216240
111216528
12121648
121316624
121416336
121516240
12161648
121617816
121618144
121619912
121620240
121621336
121622528
1216231,104
12162448
1216251,200
121626624
121627432
121628336
1216291,392
121630240
1216311,488
12163296

FAQ

What's the Least Common Multiple (LCM) of 12, 16 and 18?

LCM of 12, 16 and 18 is 144

How to find the LCM of 12, 16 and 18 by prime factorization?

Take every prime that appears in 12, 16 and 18 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² = 144.

Can you get the LCM of 12, 16 and 18 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 12 and 16 is 48, and the LCM of 48 and 18 is 144 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 144 divisible by 12, 16 and 18?

Yes, and by definition it is the smallest positive integer that is: 144 ÷ 12, 144 ÷ 16 and 144 ÷ 18 all come out whole. Any other common multiple of 12, 16 and 18 is a multiple of 144.

See Also