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


53 prime factorization25x25 multiplication chart42 multiplication tableprime factorization of 105what is the greatest common factor of 54 and 63prime factorization of 525find the prime factorization of 1267is7what is the prime factorization of 700prime factors of 58multiplication chart 200find the greatest common factor calculatorwrite 24 as a product of prime factorscommon multiples for 8 and 12gcf of 64 and 48gcf of 98what is the prime factorization of 174multiplication table chart 1 30write the prime factorization of 40write 98 as a product of prime factorslcm and gcf finderwhat is the lcm ofprime factor of 96is 157 a prime numberwhat is the greatest common factor of 128 and 192what are the prime factorization of 44what is the prime factorization of 289prime factors of 720common multiples of 6 and 15find the prime factorization of 90prime factorization of 441find the prime factorization of 35prime factorization of 52find the prime factorization of 96prime factorization of 162what is the greatest common factor of 72 and 96what is the greatest common factor of 6436-25-36the lcm of 2 and 4what is the prime factorization of 192prime factor of 57what is the lcm of 60 and 7248 as a product of prime factors12x tableswrite the prime factorization of 60prime factorization of 725prime factorization of 230225 prime factorizationwhat is the gcf of 4common denominator of 5 and 10the lcm of 2 and 4common multiples of 12 and 18prime factorization of 540find the prime factorization of 35prime factorization of 82is 251 a prime numberprime factor of 108multiplication table upto 100prime factorization of 2451-20 multiplication tableexpress 180 as a product of prime factorswhat is the prime factorization of 120what is the prime factorization of 735is 44 a prime or composite numberwhat is the gcf of 6gcf methodprime factorization of 55prime factorization of 73prime factorization of 52common multiples of 4 5 and 1036-25-36prime factorization for 8prime factorization of 525prime factorization for 210prime factors of 196