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


prime factorization of 139multiplication table chart 1-1000prime factorization of 153multiplication chart 1-25calculator gcfwhat is the prime factors of 90prime factors of 88highest common factor of 72 and 96prime factorization of 121prime factorization of 73gcf of 45 and 631-100 multiplication tableprime factorisation of 47what is prime factorization of 96what is the greatest common factor of 28 and 70the prime factorization of 90common multiples of 4 and 9find the prime factorization of 200common multiples of 2 3 and 4prime factorization 68is 30 a prime or composite numberthirtyfiveeightwhat is the prime factorization of 684what is the prime factorization of 186greatest common multiple finderprime factorization 588common multiples of 6 and 7greatest common factor of 34 and 51prime factorization 6390 prime factorizationgreatest prime factor of 68is 197 a prime numbertable of multiplication 1-100prime factorization for 55greatest common factor of 44prime factorization of 45multiplication chart that goes up to 1000write 88 as a product of prime factorsprime factorization of 46270 prime factorizationgreatest common factor of 75 and 90prime factorization of 432divisors of 496prime factor of 52common multiples of 15printable multiplication chart 1-100what is the prime factorization of 180multiplication chart 1 200prime factorization of 98the lcm of 3 and 4express 180 as a product of its prime factorscommon multiples of 4 and 11what is the lcm of 6 and 4lcm and gcf finderfind the prime factorization of 63what is the prime factorization of 240write the prime factorization of 20prime factorization of 87what is the lcm of 4 and 5is 147 a prime numberprime factors of 300multiplication table chart 1-100prime factorization of 243multiplication chart 1-30prime factorization of 44038-26-38prime factorization of 418what is the prime factorization of 21prime factorization for 300what is the prime factorization of 38what are the prime factors of 102prime factorization of 212gcf tableprime factor of 81prime factor of 95