LCM of 9 and 12


The lcm of 9 and 12 is the smallest positive integer that divides the numbers 9 and 12 without a remainder. Spelled out, it is the least common multiple of 9 and 12. Here you can find the lcm of 9 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 9 and 12, but also that of three or more integers including nine and twelve for example. Keep reading to learn everything about the lcm (9,12) and the terms related to it.

What is the LCM of 9 and 12

If you just want to know what is the least common multiple of 9 and 12, it is 36. Usually, this is written as

lcm(9,12) = 36

The lcm of 9 and 12 can be obtained like this:

  • The multiples of 9 are …, 27, 36, 45, ….
  • The multiples of 12 are …, 24, 36, 48, …
  • The common multiples of 9 and 12 are n x 36, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 9 ∩ multiples of 12 the least positive element is 36.
  • Therefore, the least common multiple of 9 and 12 is 36.

Taking the above into account you also know how to find all the common multiples of 9 and 12, not just the smallest. In the next section we show you how to calculate the lcm of nine and twelve by means of two more methods.

How to find the LCM of 9 and 12

The least common multiple of 9 and 12 can be computed by using the greatest common factor aka gcf of 9 and 12. This is the easiest approach:

lcm (9,12) = $\frac{9 \times 12}{gcf(9,12)} = \frac{108}{3}$ = 36

Alternatively, the lcm of 9 and 12 can be found using the prime factorization of 9 and 12:

  • The prime factorization of 9 is: 3 x 3
  • 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(9,9) = 36

In any case, the easiest way to compute the lcm of two numbers like 9 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 9,12. Push the button only to start over.

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

Use of LCM of 9 and 12

What is the least common multiple of 9 and 12 used for? Answer: It is helpful for adding and subtracting fractions like 1/9 and 1/12. Just multiply the dividends and divisors by 4 and 3, respectively, such that the divisors have the value of 36, the lcm of 9 and 12.

$\frac{1}{9} + \frac{1}{12} = \frac{4}{36} + \frac{3}{36} = \frac{7}{36}$. $\hspace{30px}\frac{1}{9} – \frac{1}{12} = \frac{4}{36} – \frac{3}{36} = \frac{1}{36}$.

Properties of LCM of 9 and 12

The most important properties of the lcm(9,12) are:

  • Commutative property: lcm(9,12) = lcm(12,9)
  • Associative property: lcm(9,12,n) = lcm(lcm(12,9),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 12 is 36. In common notation: lcm (9,12) = 36.

If you have been searching for lcm 9 and 12 or lcm 9 12 then you have come to the correct page, too. The same is the true if you typed lcm for 9 and 12 in your favorite search engine.

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

Questions and comments related to the lcm of 9 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 9 and 12 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


express 220 as a product of prime factorswhat is the prime factorization of 98common multiples of 5 and 9what is the prime factorization of 68the prime factorization of 84prime factorization of 190is 487 a prime numberprime factorization of 1574s times tables36-26-3640 x 40 multiplication tablewhats the prime factorization of 60multiplication table upto 100what is the prime factorization of 294is 42 a prime or composite numbercommon multiples of 7 and 14prime factorization for 55prime factors of 72common multiples of 7 and 8what is the lcm of 6 and 3prime factorization of 630common multiples of 7 and 31-100 multiplication tablemultiplication 4 times tablescommon multiples of 7printable multiplication table 1-20prime factorization 300prime factor of 56prime factors of 330gcf of 52 and 65lowest common multiple of 60 and 96the lcm of 3 and 4what is the gcf of 6prime factorization of 725prime factors of 75prime factor of 81prime factorization of 864factorization of 147prime factorization of 75multiplication table to 300prime factorization for 84times table 1-20is 14 a prime or composite numberprime factor tree of 84prime factorization of 182greatest common factor of 48 and 64multiplication chart that goes up to 1000greatest common factor of 35 and 36prime factorization of 119the prime factorization of 72prime factorization of 92the prime factorization of 90what is the prime factorization of 168what is the prime factorization of 147prime factorization of 104what is the prime factorization of 119what are the common multiples of 3 and 4prime factorization 68prime factorization of 561what is the prime factorization of 65multiplication chart 1-60prime factorization of 252the prime factorization of 88write the prime factorization of 50prime factorization of 70what is the prime factorization of 140prime factorization 160multiplication table 30x30 pdfcommon multiples of 7 and 14what is prime factorization of 84what is the prime factorization of 64prime factor of 112multiplication table 1 30 printablewrite 70 as a product of prime factors