# LCM of 12 and 16

The lcm of 12 and 16 is the smallest positive integer that divides the numbers 12 and 16 without a remainder. Spelled out, it is the least common multiple of 12 and 16. Here you can find the lcm of 12 and 16, 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 12 and 16, but also that of three or more integers including twelve and sixteen for example. Keep reading to learn everything about the lcm (12,16) and the terms related to it.

## What is the LCM of 12 and 16

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

lcm(12,16) = 48

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

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

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

## How to find the LCM of 12 and 16

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

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

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

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

In any case, the easiest way to compute the lcm of two numbers like 12 and 16 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 12,16. Push the button only to start over.

The lcm is...
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## Use of LCM of 12 and 16

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

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

## Properties of LCM of 12 and 16

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

• Commutative property: lcm(12,16) = lcm(16,12)
• Associative property: lcm(12,16,n) = lcm(lcm(16,12),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 12 and 16 is 48. In common notation: lcm (12,16) = 48.

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

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

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Posted in Least Common Multiple

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