LCM of 9 and 16


The lcm of 9 and 16 is the smallest positive integer that divides the numbers 9 and 16 without a remainder. Spelled out, it is the least common multiple of 9 and 16. Here you can find the lcm of 9 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 9 and 16, but also that of three or more integers including nine and sixteen for example. Keep reading to learn everything about the lcm (9,16) and the terms related to it.

What is the LCM of 9 and 16

If you just want to know what is the least common multiple of 9 and 16, it is 144. Usually, this is written as

lcm(9,16) = 144

The lcm of 9 and 16 can be obtained like this:

  • The multiples of 9 are …, 135, 144, 153, ….
  • The multiples of 16 are …, 128, 144, 160, …
  • The common multiples of 9 and 16 are n x 144, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 9 ∩ multiples of 16 the least positive element is 144.
  • Therefore, the least common multiple of 9 and 16 is 144.

Taking the above into account you also know how to find all the common multiples of 9 and 16, not just the smallest. In the next section we show you how to calculate the lcm of nine and sixteen by means of two more methods.

How to find the LCM of 9 and 16

The least common multiple of 9 and 16 can be computed by using the greatest common factor aka gcf of 9 and 16. This is the easiest approach:

lcm (9,16) = $\frac{9 \times 16}{gcf(9,16)} = \frac{144}{1}$ = 144

Alternatively, the lcm of 9 and 16 can be found using the prime factorization of 9 and 16:

  • The prime factorization of 9 is: 3 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(9,9) = 144

In any case, the easiest way to compute the lcm of two numbers like 9 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 9,16. Push the button only to start over.

The lcm is...
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Use of LCM of 9 and 16

What is the least common multiple of 9 and 16 used for? Answer: It is helpful for adding and subtracting fractions like 1/9 and 1/16. Just multiply the dividends and divisors by 16 and 9, respectively, such that the divisors have the value of 144, the lcm of 9 and 16.

$\frac{1}{9} + \frac{1}{16} = \frac{16}{144} + \frac{9}{144} = \frac{25}{144}$. $\hspace{30px}\frac{1}{9} – \frac{1}{16} = \frac{16}{144} – \frac{9}{144} = \frac{7}{144}$.

Properties of LCM of 9 and 16

The most important properties of the lcm(9,16) are:

  • Commutative property: lcm(9,16) = lcm(16,9)
  • Associative property: lcm(9,16,n) = lcm(lcm(16,9),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 9 and 16 is 144. In common notation: lcm (9,16) = 144.

If you have been searching for lcm 9 and 16 or lcm 9 16 then you have come to the correct page, too. The same is the true if you typed lcm for 9 and 16 in your favorite search engine.

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

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