LCM of 15 and 6


The lcm of 15 and 6 is the smallest positive integer that divides the numbers 15 and 6 without a remainder. Spelled out, it is the least common multiple of 15 and 6. Here you can find the lcm of 15 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 15 and 6, but also that of three or more integers including fifteen and six for example. Keep reading to learn everything about the lcm (15,6) and the terms related to it.

What is the LCM of 15 and 6

If you just want to know what is the least common multiple of 15 and 6, it is 30. Usually, this is written as

lcm(15,6) = 30

The lcm of 15 and 6 can be obtained like this:

  • The multiples of 15 are …, 15, 30, 45, ….
  • The multiples of 6 are …, 24, 30, 36, …
  • The common multiples of 15 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 15 ∩ multiples of 6 the least positive element is 30.
  • Therefore, the least common multiple of 15 and 6 is 30.

Taking the above into account you also know how to find all the common multiples of 15 and 6, not just the smallest. In the next section we show you how to calculate the lcm of fifteen and six by means of two more methods.

How to find the LCM of 15 and 6

The least common multiple of 15 and 6 can be computed by using the greatest common factor aka gcf of 15 and 6. This is the easiest approach:

lcm (15,6) = $\frac{15 \times 6}{gcf(15,6)} = \frac{90}{3}$ = 30

Alternatively, the lcm of 15 and 6 can be found using the prime factorization of 15 and 6:

  • The prime factorization of 15 is: 3 x 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(15,15) = 30

In any case, the easiest way to compute the lcm of two numbers like 15 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 15,6. Push the button only to start over.

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

Use of LCM of 15 and 6

What is the least common multiple of 15 and 6 used for? Answer: It is helpful for adding and subtracting fractions like 1/15 and 1/6. Just multiply the dividends and divisors by 2 and 5, respectively, such that the divisors have the value of 30, the lcm of 15 and 6.

$\frac{1}{15} + \frac{1}{6} = \frac{2}{30} + \frac{5}{30} = \frac{7}{30}$. $\hspace{30px}\frac{1}{15} – \frac{1}{6} = \frac{2}{30} – \frac{5}{30} = \frac{-3}{30}$.

Properties of LCM of 15 and 6

The most important properties of the lcm(15,6) are:

  • Commutative property: lcm(15,6) = lcm(6,15)
  • Associative property: lcm(15,6,n) = lcm(lcm(6,15),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 15 and 6 is 30. In common notation: lcm (15,6) = 30.

If you have been searching for lcm 15 and 6 or lcm 15 6 then you have come to the correct page, too. The same is the true if you typed lcm for 15 and 6 in your favorite search engine.

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

Questions and comments related to the lcm of 15 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 15 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


what is prime factorization of 120prime factorization of 154prime factorization 44gcf monomial calculatorprime factorization 35prime factors of 96common multiples of 7 and 14953 prime numberwhat is the prime factorization of 103is 251 a prime numberprime factorization of 104what is the lcm of 10 and 5write 66 as a product of prime factors100-55prime factorization 84prime factorization for 55is 30 a prime or composite numbermultiplication table chart up to 100prime factorisation of 47gcf of 81 and 6451 prime factorizationwhat is the prime factorization of 80what is the prime factorization of 110what is the prime factorization of 252what is the prime factorization of 124prime factorization of 882multiplication chart 50what is prime factorization of 120prime factorization of 375prime factorization of 82prime factors of 293prime factorization of 160multiplication table of 60multiplication table up to 10000what is the gcf of 6prime factorization 343prime factors of 72write 63 as a product of prime factorswhat is the prime factorization of 14298 prime factorization48 prime factorizationgreatest common factor of 35 and 36what is the greatest common factor of 72 and 54what is the prime factorization for 200common multiples of 3 and 7prime factorization of 55prime factorization of 41gcf of 108prime factorization of 256prime factorization of 376find the prime factorization of 58multiplication table up to 25what is the prime factorization of 210prime factorization of 45prime factors of 405greatest common factor of 45 and 72the prime factorization of 126what is the lcm of 2 and 884 as a product of prime factorsgcf and lcm finder56 as a product of prime factorswhat is the lcm of 3 and 7find the prime factorization of 52multiplication table 1-30highest common factor calculator 3 numberswhat is the greatest common factor of 36 and 90hcf of 45 and 72what is the greatest common factor of 72 and 54gcf of 70 and 989times tableprime factorization of 971-20 multiplication chartsmallest common multiple of 36 and 60prime factorization of 170