# LCM of 16 and 12

The lcm of 16 and 12 is the smallest positive integer that divides the numbers 16 and 12 without a remainder. Spelled out, it is the least common multiple of 16 and 12. Here you can find the lcm of 16 and 12, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the lcm of 16 and 12, but also that of three or more integers including sixteen and twelve for example. Keep reading to learn everything about the lcm (16,12) and the terms related to it.

## What is the LCM of 16 and 12

If you just want to know what is the least common multiple of 16 and 12, it is 48. Usually, this is written as

lcm(16,12) = 48

The lcm of 16 and 12 can be obtained like this:

• The multiples of 16 are …, 32, 48, 64, ….
• The multiples of 12 are …, 36, 48, 60, …
• The common multiples of 16 and 12 are n x 48, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
• In the intersection multiples of 16 ∩ multiples of 12 the least positive element is 48.
• Therefore, the least common multiple of 16 and 12 is 48.

Taking the above into account you also know how to find all the common multiples of 16 and 12, not just the smallest. In the next section we show you how to calculate the lcm of sixteen and twelve by means of two more methods.

## How to find the LCM of 16 and 12

The least common multiple of 16 and 12 can be computed by using the greatest common factor aka gcf of 16 and 12. This is the easiest approach:

lcm (16,12) = $\frac{16 \times 12}{gcf(16,12)} = \frac{192}{4}$ = 48

Alternatively, the lcm of 16 and 12 can be found using the prime factorization of 16 and 12:

• The prime factorization of 16 is: 2 x 2 x 2 x 2
• The prime factorization of 12 is: 2 x 2 x 3
• Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(16,16) = 48

In any case, the easiest way to compute the lcm of two numbers like 16 and 12 is by using our calculator below. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 16,12. Push the button only to start over.

The lcm is...
Frequently searched terms on our site also include:

## Use of LCM of 16 and 12

What is the least common multiple of 16 and 12 used for? Answer: It is helpful for adding and subtracting fractions like 1/16 and 1/12. Just multiply the dividends and divisors by 3 and 4, respectively, such that the divisors have the value of 48, the lcm of 16 and 12.

$\frac{1}{16} + \frac{1}{12} = \frac{3}{48} + \frac{4}{48} = \frac{7}{48}$. $\hspace{30px}\frac{1}{16} – \frac{1}{12} = \frac{3}{48} – \frac{4}{48} = \frac{-1}{48}$.

## Properties of LCM of 16 and 12

The most important properties of the lcm(16,12) are:

• Commutative property: lcm(16,12) = lcm(12,16)
• Associative property: lcm(16,12,n) = lcm(lcm(12,16),n) $\hspace{10px}n\neq 0 \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$

The associativity is particularly useful to get the lcm of three or more numbers; our calculator makes use of it.

To sum up, the lcm of 16 and 12 is 48. In common notation: lcm (16,12) = 48.

If you have been searching for lcm 16 and 12 or lcm 16 12 then you have come to the correct page, too. The same is the true if you typed lcm for 16 and 12 in your favorite search engine.

Note that you can find the least common multiple of many integer pairs including sixteen / twelve by using the search form in the sidebar of this page.

Questions and comments related to the lcm of 16 and 12 are really appreciated. Use the form below or send us a mail to get in touch.

Please hit the sharing buttons if our article about the least common multiple of 16 and 12 has been useful to you, and make sure to bookmark our site.

Posted in Least Common Multiple

## Related pages

prime factorization of 184prime factorization 240write 18 as a product of prime factorsprime factors of 140multiplication chart up to 500prime factorization 51greatest common factor of 48 and 64what are prime factors of 75what is prime factorization of 120prime factors of 88the prime factorization of 65greatest common factor of 121prime factorization of 79is 191 a prime numberfind the prime factorization of 3684-35108 as a product of prime factorsprime factorization of 72gcf of 81 and 64220 as a product of prime factorscommon multiples of 6greatest common factor of 28 and 44factor tree for 63prime factors of 56multiplication 4 times tablesprime factorization for 140multiplication table upto 20prime factorization for 90lowest common multiple of 72 and 120what is the prime factorization of 61what is the greatest common factor of 72 and 54the prime factorization of 92prime factorization for 84what is the prime factorization of 328whats a prime factor25 by 25 multiplication chartwhat is the prime factorization of 21prime factorization of 378what is the lcm of 4 and 109x tablewhat are the prime factors of 88is 105 a composite numberwhat is the prime factorization of 135what is the gcf ofwhat is the prime factorization of 293the lcm of 4 and 10what are the prime factors of 125what is the lcm of 2 and 12greatest common multiple finder1 30 multiplication chartgreatest common factor of 36 and 44multiplication chart to 300determine the prime factorization of 88printable multiplication chart 1-20prime factorization of 256what is the greatest common factor of 32 and 56multiplication table 1-20 printableprime factorization 350what is the prime factorization of 20prime factorization of 68453 prime factorizationprime factorization of 198prime factorization for 108prime factors of 75the prime factorization of 225what is the prime factorization of 97prime factorization 67greatest common factor of 48 and 64prime factorization of 400 using exponentsprime factorization of 288prime factorization 99