LCM of 8 and 12


The lcm of 8 and 12 is the smallest positive integer that divides the numbers 8 and 12 without a remainder. Spelled out, it is the least common multiple of 8 and 12. Here you can find the lcm of 8 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 8 and 12, but also that of three or more integers including eight and twelve for example. Keep reading to learn everything about the lcm (8,12) and the terms related to it.

What is the LCM of 8 and 12

If you just want to know what is the least common multiple of 8 and 12, it is 24. Usually, this is written as

lcm(8,12) = 24

The lcm of 8 and 12 can be obtained like this:

  • The multiples of 8 are …, 16, 24, 32, ….
  • The multiples of 12 are …, 12, 24, 36, …
  • The common multiples of 8 and 12 are n x 24, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 8 ∩ multiples of 12 the least positive element is 24.
  • Therefore, the least common multiple of 8 and 12 is 24.

Taking the above into account you also know how to find all the common multiples of 8 and 12, not just the smallest. In the next section we show you how to calculate the lcm of eight and twelve by means of two more methods.

How to find the LCM of 8 and 12

The least common multiple of 8 and 12 can be computed by using the greatest common factor aka gcf of 8 and 12. This is the easiest approach:

lcm (8,12) = $\frac{8 \times 12}{gcf(8,12)} = \frac{96}{4}$ = 24

Alternatively, the lcm of 8 and 12 can be found using the prime factorization of 8 and 12:

  • The prime factorization of 8 is: 2 x 2 x 2
  • 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(8,8) = 24

In any case, the easiest way to compute the lcm of two numbers like 8 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 8,12. Push the button only to start over.

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

Use of LCM of 8 and 12

What is the least common multiple of 8 and 12 used for? Answer: It is helpful for adding and subtracting fractions like 1/8 and 1/12. Just multiply the dividends and divisors by 3 and 2, respectively, such that the divisors have the value of 24, the lcm of 8 and 12.

$\frac{1}{8} + \frac{1}{12} = \frac{3}{24} + \frac{2}{24} = \frac{5}{24}$. $\hspace{30px}\frac{1}{8} – \frac{1}{12} = \frac{3}{24} – \frac{2}{24} = \frac{1}{24}$.

Properties of LCM of 8 and 12

The most important properties of the lcm(8,12) are:

  • Commutative property: lcm(8,12) = lcm(12,8)
  • Associative property: lcm(8,12,n) = lcm(lcm(12,8),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 8 and 12 is 24. In common notation: lcm (8,12) = 24.

If you have been searching for lcm 8 and 12 or lcm 8 12 then you have come to the correct page, too. The same is the true if you typed lcm for 8 and 12 in your favorite search engine.

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

Questions and comments related to the lcm of 8 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 8 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


prime factorization 300prime factor of 102hcf of 45 and 72what is the lcm of 6 and 4express 126 as a product of prime numbers63 prime factorizationprime factors of 330what is the lcm of 6what is the prime factorization of 91prime factorizations of 72gcf of 81 and 48write 60 as a product of prime factors20 x 20 times tableprime factorization of 700printable multiplication table 1-100the prime factorization of 65finding the gcf calculatorprime factorization of 170what is the prime factorization of 160what is the prime factorization of 675prime factorization of 250prime factorization of 322what is the prime factorization of 75prime factorizations of 72what is the prime factorization of 138find the gcf of 48 and 72what is the greatest common factor of 128 and 192what is the gcf of 60 and 72prime factorization of 147lcm of 5 7multiplication table 1-13prime factorization 51prime factorization of 42 using exponentsgreatest common factor of 121greatest common factor of 42 and 63what is the greatest common factor of 96 and 64what is the prime factorization of 625common multiples of 2 and 4least common multiples of 8 and 12prime factorization 150common multiples of 24 and 36 from 1 to 100what is the highest common factor of 48 and 88prime factorization for 60prime factorization for 19660 prime factorizationwhat are the prime factors of 105easiest way to find greatest common factor144 prime factorizationprime factorization of 399prime factorization of 712x times tablesis 24 a prime or composite numberprime factorization of 28937-100953 prime numberthirtyeightfivewhat is the greatest common factor of 24 and 108prime factors of 700what is the gcf of 96 48 and 84gcf of 75 and 60prime factorization of 484what is the greatest common factor of 24 and 36common multiples of 8 and 3is 19 a prime or composite numbercommon multiples of 7what is the prime factor of 92what is prime factorization of 120greatest common factor of 28 and 70prime factorization of 170prime factorizations of 7236-25-36