LCM of 6 and 8


The lcm of 6 and 8 is the smallest positive integer that divides the numbers 6 and 8 without a remainder. Spelled out, it is the least common multiple of 6 and 8. Here you can find the lcm of 6 and 8, 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 8, but also that of three or more integers including six and eight for example. Keep reading to learn everything about the lcm (6,8) and the terms related to it.

What is the LCM of 6 and 8

If you just want to know what is the least common multiple of 6 and 8, it is 24. Usually, this is written as

lcm(6,8) = 24

The lcm of 6 and 8 can be obtained like this:

  • The multiples of 6 are …, 18, 24, 30, ….
  • The multiples of 8 are …, 16, 24, 32, …
  • The common multiples of 6 and 8 are n x 24, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 6 ∩ multiples of 8 the least positive element is 24.
  • Therefore, the least common multiple of 6 and 8 is 24.

Taking the above into account you also know how to find all the common multiples of 6 and 8, not just the smallest. In the next section we show you how to calculate the lcm of six and eight by means of two more methods.

How to find the LCM of 6 and 8

The least common multiple of 6 and 8 can be computed by using the greatest common factor aka gcf of 6 and 8. This is the easiest approach:

lcm (6,8) = $\frac{6 \times 8}{gcf(6,8)} = \frac{48}{2}$ = 24

Alternatively, the lcm of 6 and 8 can be found using the prime factorization of 6 and 8:

  • The prime factorization of 6 is: 2 x 3
  • The prime factorization of 8 is: 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(6,6) = 24

In any case, the easiest way to compute the lcm of two numbers like 6 and 8 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 6,8. Push the button only to start over.

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

Use of LCM of 6 and 8

What is the least common multiple of 6 and 8 used for? Answer: It is helpful for adding and subtracting fractions like 1/6 and 1/8. Just multiply the dividends and divisors by 4 and 3, respectively, such that the divisors have the value of 24, the lcm of 6 and 8.

$\frac{1}{6} + \frac{1}{8} = \frac{4}{24} + \frac{3}{24} = \frac{7}{24}$. $\hspace{30px}\frac{1}{6} – \frac{1}{8} = \frac{4}{24} – \frac{3}{24} = \frac{1}{24}$.

Properties of LCM of 6 and 8

The most important properties of the lcm(6,8) are:

  • Commutative property: lcm(6,8) = lcm(8,6)
  • Associative property: lcm(6,8,n) = lcm(lcm(8,6),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 8 is 24. In common notation: lcm (6,8) = 24.

If you have been searching for lcm 6 and 8 or lcm 6 8 then you have come to the correct page, too. The same is the true if you typed lcm for 6 and 8 in your favorite search engine.

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

Questions and comments related to the lcm of 6 and 8 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 8 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 439x tablefactorization of 147prime factorization for 46prime factorization of 232gcf of 52 and 65what is the greatest common factor of 86 and 94greatest common factors calculatortable of multiplication 1-100determine the prime factorization of 8896 factor treemultiplication table 30x30gcf of 45 and 75prime factorization of 153prime factorization of 612greatest common factor of 35 and 63is 196 a prime numberwhat is the greatest common factor of 128 and 19242 prime factorizationprime factor of 112what are the prime factors of 88what is the gcf of 2what are the prime factors of 385prime factors of 95what is the gcf of 96 and 84what is the greatest common factor of 24 and 36what is prime factorization of 52common denominator of 7 and 12common multiples of 4 and 6factor tree for 96prime factorization for 96multiplication chart that goes up to 100prime factorization 49what is the gcf of 84 and 962x times tablesgcf of 70 and 98common multiples of 10 and 15what is the prime factorization for 132gcf of 121the lcm of 2 and 420 by 20 multiplication chart printablewhat is the prime factorization 56common multiples of 7 and 8what is the greatest common factor of 72 and 96is 63 a prime or composite numberis 19 a prime or composite numberfind the prime factorization of 28prime factor of 98prime factorization 92what is prime factorization of 96gcf of 48 and 64what is the gcf of 96 and 84smallest common multiple of 36 and 60is 50 a prime or composite numberwhat is the prime factorization of 118is 35 a prime or composite numberwhat is the greatest common factor of 42 and 7242 prime factorizationwhat are the prime factors of 102is 467 a prime numberis 847 a prime numberwhat is prime factorization of 63what is the gcf of 9multiplication table 30x30 pdfgcf of 144prime factorization of 70prime factorization of 34356 as a product of prime factorsgreatest common factor of 42 and 56what is the prime factorization of 828the prime factorization of 72find the prime factorization of 144prime factorization of 344what is the prime factorization of 133multiplication chart up to 200what is the prime factorization of 120what is the prime factorization of 164