LCM of 7 and 8


The lcm of 7 and 8 is the smallest positive integer that divides the numbers 7 and 8 without a remainder. Spelled out, it is the least common multiple of 7 and 8. Here you can find the lcm of 7 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 7 and 8, but also that of three or more integers including seven and eight for example. Keep reading to learn everything about the lcm (7,8) and the terms related to it.

What is the LCM of 7 and 8

If you just want to know what is the least common multiple of 7 and 8, it is 56. Usually, this is written as

lcm(7,8) = 56

The lcm of 7 and 8 can be obtained like this:

  • The multiples of 7 are …, 49, 56, 63, ….
  • The multiples of 8 are …, 48, 56, 64, …
  • The common multiples of 7 and 8 are n x 56, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 7 ∩ multiples of 8 the least positive element is 56.
  • Therefore, the least common multiple of 7 and 8 is 56.

Taking the above into account you also know how to find all the common multiples of 7 and 8, not just the smallest. In the next section we show you how to calculate the lcm of seven and eight by means of two more methods.

How to find the LCM of 7 and 8

The least common multiple of 7 and 8 can be computed by using the greatest common factor aka gcf of 7 and 8. This is the easiest approach:

lcm (7,8) = $\frac{7 \times 8}{gcf(7,8)} = \frac{56}{1}$ = 56

Alternatively, the lcm of 7 and 8 can be found using the prime factorization of 7 and 8:

  • The prime factorization of 7 is: 7
  • 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(7,7) = 56

In any case, the easiest way to compute the lcm of two numbers like 7 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 7,8. Push the button only to start over.

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

Use of LCM of 7 and 8

What is the least common multiple of 7 and 8 used for? Answer: It is helpful for adding and subtracting fractions like 1/7 and 1/8. Just multiply the dividends and divisors by 8 and 7, respectively, such that the divisors have the value of 56, the lcm of 7 and 8.

$\frac{1}{7} + \frac{1}{8} = \frac{8}{56} + \frac{7}{56} = \frac{15}{56}$. $\hspace{30px}\frac{1}{7} – \frac{1}{8} = \frac{8}{56} – \frac{7}{56} = \frac{1}{56}$.

Properties of LCM of 7 and 8

The most important properties of the lcm(7,8) are:

  • Commutative property: lcm(7,8) = lcm(8,7)
  • Associative property: lcm(7,8,n) = lcm(lcm(8,7),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 7 and 8 is 56. In common notation: lcm (7,8) = 56.

If you have been searching for lcm 7 and 8 or lcm 7 8 then you have come to the correct page, too. The same is the true if you typed lcm for 7 and 8 in your favorite search engine.

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

Questions and comments related to the lcm of 7 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 7 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


the prime factorization of 200what is the greatest common factor of 128 and 192multiplication table 1-20lcm of 150147 prime numberlcm and gcf finderwrite 72 as a product of prime factorswhat is the lcm of 1238 prime factorizationwhat is the prime factorization of 201write the prime factorization of 50what is the greatest prime factor of 96140 prime factorization100-82what is the prime factorization of 198greatest common factor of 45 and 72find the prime factorization of 225is 983 a prime numberwhat is prime factorization of 70what is prime factorization of 72prime factorization of 103prime factorization of 245prime factorization of 289multiplication chart to 200prime factorization 300express 56 as a product of its prime factorsmultiplication table 1 30 printabletable of multiplication 1-100what is the greatest common factor of 17 and 3450 prime factorizationmultiplication table up to 25prime factors of 65what is the prime factorization of 312prime factorization 132multiplication table 40x40prime factorization of 24490-5420primeprime factorization 60the lcm of 3 and 5multiplication table 20x20 printablewhat is the gcf of 56 and 98prime factors of 210prime factorization of 74what are common multiples of 3 and 4common multiples of 10prime factorization of 47the prime factorization of 72prime factorization of 60gcf tablemultiplication table 1-50multiples of elevencommon multiples of 4 and 775 prime factorizationlcm 5 7multiplication table upto 100prime factors of 735greatest common factor of 48 and 80what is the prime factorization of 192gcf and lcm of 36 and 45prime factorization of 245prime factorization of 720greatest common factor of 45 and 72what are the prime factors of 65find the prime factorization of 175common multiples of 8 and 10prime factors of 58what is the prime factorization of 53what is the prime factorization of 54what is the prime factorization of 289prime factorization of 41