LCM of 6 and 10


The lcm of 6 and 10 is the smallest positive integer that divides the numbers 6 and 10 without a remainder. Spelled out, it is the least common multiple of 6 and 10. Here you can find the lcm of 6 and 10, 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 10, but also that of three or more integers including six and ten for example. Keep reading to learn everything about the lcm (6,10) and the terms related to it.

What is the LCM of 6 and 10

If you just want to know what is the least common multiple of 6 and 10, it is 30. Usually, this is written as

lcm(6,10) = 30

The lcm of 6 and 10 can be obtained like this:

  • The multiples of 6 are …, 24, 30, 36, ….
  • The multiples of 10 are …, 20, 30, 40, …
  • The common multiples of 6 and 10 are n x 30, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 6 ∩ multiples of 10 the least positive element is 30.
  • Therefore, the least common multiple of 6 and 10 is 30.

Taking the above into account you also know how to find all the common multiples of 6 and 10, not just the smallest. In the next section we show you how to calculate the lcm of six and ten by means of two more methods.

How to find the LCM of 6 and 10

The least common multiple of 6 and 10 can be computed by using the greatest common factor aka gcf of 6 and 10. This is the easiest approach:

lcm (6,10) = $\frac{6 \times 10}{gcf(6,10)} = \frac{60}{2}$ = 30

Alternatively, the lcm of 6 and 10 can be found using the prime factorization of 6 and 10:

  • The prime factorization of 6 is: 2 x 3
  • The prime factorization of 10 is: 2 x 5
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(6,6) = 30

In any case, the easiest way to compute the lcm of two numbers like 6 and 10 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 6,10. Push the button only to start over.

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

Use of LCM of 6 and 10

What is the least common multiple of 6 and 10 used for? Answer: It is helpful for adding and subtracting fractions like 1/6 and 1/10. Just multiply the dividends and divisors by 5 and 3, respectively, such that the divisors have the value of 30, the lcm of 6 and 10.

$\frac{1}{6} + \frac{1}{10} = \frac{5}{30} + \frac{3}{30} = \frac{8}{30}$. $\hspace{30px}\frac{1}{6} – \frac{1}{10} = \frac{5}{30} – \frac{3}{30} = \frac{2}{30}$.

Properties of LCM of 6 and 10

The most important properties of the lcm(6,10) are:

  • Commutative property: lcm(6,10) = lcm(10,6)
  • Associative property: lcm(6,10,n) = lcm(lcm(10,6),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 10 is 30. In common notation: lcm (6,10) = 30.

If you have been searching for lcm 6 and 10 or lcm 6 10 then you have come to the correct page, too. The same is the true if you typed lcm for 6 and 10 in your favorite search engine.

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

Questions and comments related to the lcm of 6 and 10 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 10 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


highest common factor of 72 and 96what is the lcm of 2 and 8what is the gcf of 9multiplication table 1-15what is the gcf of 72 and 36write 63 as a product of prime factorsprime factorization of 280prime factorization 150prime factorization of 299gcf of 45 and 75prime factorization of 41common multiples of 2 and 7prime factorization of 196what is the prime factorization of 9230x30 multiplication tableis thirteen a prime numberfind the prime factorization of 126times table 30x30is 173 a prime numbergcf of 70 and 98prime factorization of 33prime factorization of 162the prime factorization of 72prime factorization 84prime factorization of 900times tables 4xgreatest common factor of 48 and 54is 67 a prime or composite numbergcf of 69 and 9220 by 20 multiplication chartgcf of 108common multiples of 9 and 12prime factorization of 42 using exponentslcm of 120 and 150prime factors of 420100-7220 by 20 multiplication chartwhat is prime factorization of 70what is the prime factorization of 650the prime factorization of 5138-26-38prime factorization of 720what is the prime factor of 92express 180 as a product of prime factorsprime factors of 112greatest prime factor of 68common multiples of 4 and 8find the prime factorization of 144prime factorization of 38prime factors of 980highest common factor of 56what is the prime factorization of 61gcf of 45 and 6398 prime factorizationprime factorization for 39what is the lowest common multiple of 60 and 96times table chart 1 1000prime factors of 46220 x 20 times tablefind the prime factorization of 200whats the prime factorization of 16find the prime factorization of 36find the prime factorization of 42what is the gcf of 84prime factorization 85what is prime factorization of 64what is the prime factorization of 525prime factorization for 90prime factors of 92greatest common factor of 72 and 96prime factorization of 143what is the gcf of 56 and 96what are prime factors of 8420 x 20 times tablewhat are the prime factors of 132what is the gcf of 4