LCM of 5 and 6


The lcm of 5 and 6 is the smallest positive integer that divides the numbers 5 and 6 without a remainder. Spelled out, it is the least common multiple of 5 and 6. Here you can find the lcm of 5 and 6, 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 5 and 6, but also that of three or more integers including five and six for example. Keep reading to learn everything about the lcm (5,6) and the terms related to it.

What is the LCM of 5 and 6

If you just want to know what is the least common multiple of 5 and 6, it is 30. Usually, this is written as

lcm(5,6) = 30

The lcm of 5 and 6 can be obtained like this:

  • The multiples of 5 are …, 25, 30, 35, ….
  • The multiples of 6 are …, 24, 30, 36, …
  • The common multiples of 5 and 6 are n x 30, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 5 ∩ multiples of 6 the least positive element is 30.
  • Therefore, the least common multiple of 5 and 6 is 30.

Taking the above into account you also know how to find all the common multiples of 5 and 6, not just the smallest. In the next section we show you how to calculate the lcm of five and six by means of two more methods.

How to find the LCM of 5 and 6

The least common multiple of 5 and 6 can be computed by using the greatest common factor aka gcf of 5 and 6. This is the easiest approach:

lcm (5,6) = $\frac{5 \times 6}{gcf(5,6)} = \frac{30}{1}$ = 30

Alternatively, the lcm of 5 and 6 can be found using the prime factorization of 5 and 6:

  • The prime factorization of 5 is: 5
  • The prime factorization of 6 is: 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(5,5) = 30

In any case, the easiest way to compute the lcm of two numbers like 5 and 6 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 5,6. Push the button only to start over.

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

Use of LCM of 5 and 6

What is the least common multiple of 5 and 6 used for? Answer: It is helpful for adding and subtracting fractions like 1/5 and 1/6. Just multiply the dividends and divisors by 6 and 5, respectively, such that the divisors have the value of 30, the lcm of 5 and 6.

$\frac{1}{5} + \frac{1}{6} = \frac{6}{30} + \frac{5}{30} = \frac{11}{30}$. $\hspace{30px}\frac{1}{5} – \frac{1}{6} = \frac{6}{30} – \frac{5}{30} = \frac{1}{30}$.

Properties of LCM of 5 and 6

The most important properties of the lcm(5,6) are:

  • Commutative property: lcm(5,6) = lcm(6,5)
  • Associative property: lcm(5,6,n) = lcm(lcm(6,5),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 5 and 6 is 30. In common notation: lcm (5,6) = 30.

If you have been searching for lcm 5 and 6 or lcm 5 6 then you have come to the correct page, too. The same is the true if you typed lcm for 5 and 6 in your favorite search engine.

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

Questions and comments related to the lcm of 5 and 6 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 5 and 6 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


common multiples of 4 and 11gcf of 56 and 72what is prime factorization of 96find the prime factorization of 49prime factorization for 85what is the greatest common factor of 42 and 70gcf of 28 and 42prime factor of 95what is the prime factorization of 99what is the lcm of 5 and 7greatest common factor of 24 and 108prime factorization for 196prime factorization for 126prime factorization of 110the prime factorization of 180what is a prime factorization of 72what is the greatest common factor of 34 and 51write 36 as a product of its prime factorshcf of 60 and 75gcf of 96 and 120prime factorization of 270what are the prime factors of 105prime factorization of 300multiplication tables 1-15prime factorization of 612what is the prime factorization of 735what is the prime factorization of 245is 125 a prime or composite numberprime factorization 105what is the largest prime factor of 200prime factorization of 312what is the lcm ofthe prime factorization of 175what is the lcm of 60 and 72prime factorization for 76common multiples of 7lcm of 63what is the prime factorization of 1051-30 multiplication chartgcf of 52 and 65prime factorization of 176is 161 a prime numberthe prime factorization of 105find the prime factorization of 126prime factorization of 55is 21 a prime number or a composite numbersmallest common multiple of 36 and 60prime factorization 54common multiples of 10 and 15what is the gcf of 6define lowest common multiplewhat is the prime factorization of 198what are the prime factors of 66what is the lcm of 3gcf of 54 and 63common multiples of 4what is the prime factorization of 138gcf of 98prime factorization of 58what is the prime factorization of 81multiplication chart 3096 prime factorization45 prime factorizationwhat is the lcm of 9is 87 a prime or composite numberexpress 180 as a product of prime factorsprime factorization of 144prime factorization of 1902x times tableswhat is the prime factorization of 66the prime factorization of 175multiplication table 1-100prime factorization of 67find the prime factorization of 105prime factors of 49gcf of 90 and 75what is the prime factorization of 310prime factorization 135