LCM of 6 and 9


The lcm of 6 and 9 is the smallest positive integer that divides the numbers 6 and 9 without a remainder. Spelled out, it is the least common multiple of 6 and 9. Here you can find the lcm of 6 and 9, 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 6 and 9, but also that of three or more integers including six and nine for example. Keep reading to learn everything about the lcm (6,9) and the terms related to it.

What is the LCM of 6 and 9

If you just want to know what is the least common multiple of 6 and 9, it is 18. Usually, this is written as

lcm(6,9) = 18

The lcm of 6 and 9 can be obtained like this:

  • The multiples of 6 are …, 12, 18, 24, ….
  • The multiples of 9 are …, 9, 18, 27, …
  • The common multiples of 6 and 9 are n x 18, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 6 ∩ multiples of 9 the least positive element is 18.
  • Therefore, the least common multiple of 6 and 9 is 18.

Taking the above into account you also know how to find all the common multiples of 6 and 9, not just the smallest. In the next section we show you how to calculate the lcm of six and nine by means of two more methods.

How to find the LCM of 6 and 9

The least common multiple of 6 and 9 can be computed by using the greatest common factor aka gcf of 6 and 9. This is the easiest approach:

lcm (6,9) = $\frac{6 \times 9}{gcf(6,9)} = \frac{54}{3}$ = 18

Alternatively, the lcm of 6 and 9 can be found using the prime factorization of 6 and 9:

  • The prime factorization of 6 is: 2 x 3
  • The prime factorization of 9 is: 3 x 3
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(6,6) = 18

In any case, the easiest way to compute the lcm of two numbers like 6 and 9 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 6,9. Push the button only to start over.

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

Use of LCM of 6 and 9

What is the least common multiple of 6 and 9 used for? Answer: It is helpful for adding and subtracting fractions like 1/6 and 1/9. Just multiply the dividends and divisors by 3 and 2, respectively, such that the divisors have the value of 18, the lcm of 6 and 9.

$\frac{1}{6} + \frac{1}{9} = \frac{3}{18} + \frac{2}{18} = \frac{5}{18}$. $\hspace{30px}\frac{1}{6} – \frac{1}{9} = \frac{3}{18} – \frac{2}{18} = \frac{1}{18}$.

Properties of LCM of 6 and 9

The most important properties of the lcm(6,9) are:

  • Commutative property: lcm(6,9) = lcm(9,6)
  • Associative property: lcm(6,9,n) = lcm(lcm(9,6),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 6 and 9 is 18. In common notation: lcm (6,9) = 18.

If you have been searching for lcm 6 and 9 or lcm 6 9 then you have come to the correct page, too. The same is the true if you typed lcm for 6 and 9 in your favorite search engine.

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

Questions and comments related to the lcm of 6 and 9 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 6 and 9 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


prime factorization of 95prime factorization for 125what is the prime factorization of 192prime factor of 92what is the prime factorization of 2800gcf calculaterhcf of 45 and 72prime factorization of 560what is the prime factorization of 121gcf of 26prime factors of 91what is the prime factorization for 200is 185 a prime numbergcf of 48 and 64prime factors of 9181-64prime factorization of 1000thirtyfiveeightthe prime factorization of 200multiplication table 0-100prime factorization of 231prime factorization 88least common multiples chartwhat is 24 as a product of prime factorsfind the prime factorization of 52what is the greatest common factor of 56 and 64what is the gcf of 54 and 84gcf of 64 and 48prime factors of 294prime factorization of 164multiplication table 40 x 40highest common factor of 72 and 96prime factorization of 630lcm of 150is 121 prime numberlowest common multiple of 60 and 96is 83 a prime or composite numbercommon multiples of 9 and 12find the prime factorization of 49what are the prime factors of 108the prime factorization of 95prime factorization of 2200prime factorization 98what is the greatest common factor of 54 and 368x times tablewhat is the prime factorization of 41prime factorization for 144prime factorization for 180prime factorization of 190100-81what is the prime factorization of 205what is the greatest common factor of 70 and 42prime factorization 198prime factorization of 192prime factor of 56greatest prime factor of 68prime factors of 49what are the prime factors of 108prime factors of 56multiplication table 25x25 printableprime factorization 3001-100 multiplication tabletimes table 30x30write 24 as a product of prime factorsprime factorization of 82common denominator of 5 and 10what is the greatest common factor of 35 and 49multiplication table up to 25what is the gcf of 60 and 72find the prime factorization of 99what is the prime factorization of 192