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...
Frequently searched terms on our site also include:

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.

Questions and comments related to the lcm of 9 and 16 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 9 and 16 has been useful to you, and make sure to bookmark our site.

Thanks for your visit.

Print Friendly, PDF & Email
Posted in Least Common Multiple

Leave a Reply

Your email address will not be published. Required fields are marked *

*


Related pages


what are the prime factors of 64multiplication chart 1-30what is the lcm of 2 and 12prime factorization of 561the prime factorization of 200what is the prime factorization of 232prime factor of 196gcf of 98what is the prime factor of 56what are the prime factors of 102prime factorization of 153is 509 a prime number196 prime factorizationprime factorization of 136prime factorization of 128prime factors of 490the prime factorization of 85multiplication table 40what is the prime factorization of 64what is the prime factor of 92what is the prime factorization of 176greatest common factor of 56 and 42prime factor of 95what is the prime factorization for 38greatest common factor of 34 and 51common multiples of 9prime factorization of 61multiplication table 1-20 printableprime factorization of 254what is the lcm of 3 and 7common multiples of 2 and 496 factor treewhats the prime factorization of 60whats prime factorizationwhat is the prime factorization of 650greatest common factor of 36 and 44what is the prime factorization of 190write 54 as a product of prime factorswhat is the gcf of 56 and 96what is the prime factorization of 118is 39 a prime or composite numberis 229 a prime numberprime factorization of 157prime factorization for 46factorization of 147multiplication table of 60prime factorization for 90prime factorization of 540prime factorization of 289prime factorization of 61greatest prime factor of 38702 756 5346prime factorization of 85is 139 a prime numberis 24 a prime number or a composite numberprime factors of 74multiplication chart 1 500common multiples of 7 and 14what is the prime factorization of 1000prime factorization of 80multiplication table 20x20 printableprime factorization of 71what is the prime factorization of 92prime factorization of 864multiplication chart that goes to 100multiplication tables upto 20 pdfprime factorization of 55find the prime factorization of 175100-74factor tree for 96what is the prime factorization of 68prime factor of 196multiplication chart to 20factor tree of 96multiplication 4 times tableslcm and gcf finderprime factorization for 44