LCM of 6 and 3


The lcm of 6 and 3 is the smallest positive integer that divides the numbers 6 and 3 without a remainder. Spelled out, it is the least common multiple of 6 and 3. Here you can find the lcm of 6 and 3, 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 3, but also that of three or more integers including six and three for example. Keep reading to learn everything about the lcm (6,3) and the terms related to it.

What is the LCM of 6 and 3

If you just want to know what is the least common multiple of 6 and 3, it is 6. Usually, this is written as

lcm(6,3) = 6

The lcm of 6 and 3 can be obtained like this:

  • The multiples of 6 are …, 0, 6, 12, ….
  • The multiples of 3 are …, 3, 6, 9, …
  • The common multiples of 6 and 3 are n x 6, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 6 ∩ multiples of 3 the least positive element is 6.
  • Therefore, the least common multiple of 6 and 3 is 6.

Taking the above into account you also know how to find all the common multiples of 6 and 3, not just the smallest. In the next section we show you how to calculate the lcm of six and three by means of two more methods.

How to find the LCM of 6 and 3

The least common multiple of 6 and 3 can be computed by using the greatest common factor aka gcf of 6 and 3. This is the easiest approach:

lcm (6,3) = $\frac{6 \times 3}{gcf(6,3)} = \frac{18}{3}$ = 6

Alternatively, the lcm of 6 and 3 can be found using the prime factorization of 6 and 3:

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

In any case, the easiest way to compute the lcm of two numbers like 6 and 3 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 6,3. Push the button only to start over.

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

Use of LCM of 6 and 3

What is the least common multiple of 6 and 3 used for? Answer: It is helpful for adding and subtracting fractions like 1/6 and 1/3. Just multiply the dividends and divisors by 1 and 2, respectively, such that the divisors have the value of 6, the lcm of 6 and 3.

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

Properties of LCM of 6 and 3

The most important properties of the lcm(6,3) are:

  • Commutative property: lcm(6,3) = lcm(3,6)
  • Associative property: lcm(6,3,n) = lcm(lcm(3,6),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 3 is 6. In common notation: lcm (6,3) = 6.

If you have been searching for lcm 6 and 3 or lcm 6 3 then you have come to the correct page, too. The same is the true if you typed lcm for 6 and 3 in your favorite search engine.

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

Questions and comments related to the lcm of 6 and 3 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 3 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 300what is the greatest common factor of 48 and 64prime factorization of 3761-100 multiplication tablegcf monomial calculatoris 158 a prime numberfind the greatest common factor of 270 and 360what is the greatest common factor of 54 and 36what is the gcf of 84prime factors of numbers 1 100what is the greatest common factor of 32 and 56multiples of elevenprintable multiplication table 1-100prime factorization of 396prime factorization of 44prime factors of 92factor tree for 9660 multiplication tablethe prime factorization of 245prime factorization 90multiples of tenwhat is the prime factorization of 48what is the greatest common factor of 42 and 63what is prime factorization of 96gcf of 28 and 42write 66 as a product of prime factorsgcf of 96 and 144common denominator of 5 and 10common multiples of 5 and 7multiplication chart to 20200 multiplication chartprime factorization for 44what is the prime factorization of 462what is the prime factorization of 75hcf of 60 and 75prime factorization of 400 using exponentsgreatest common factor of 34 and 51what is the prime factorization of 126prime factor of 102common multiples of 12 and 18what is the prime factorization of 360multiplication chart 200what are the prime factorization of 81what is the prime factorization of 85gcf and lcm finder45 prime factorizationprime factorization of 97gcf of 40 and 64prime factorization of 55gcf of 49 and 81what is the greatest common factor of 24 and 72prime factorization for 65prime factorization for 54multiplication table 1-40is 181 a prime numbercommon multiples of 6find the prime factorization of 4920 by 20 multiplication chart printableprime factorization of 153write 88 as a product of prime factorswrite 72 as a product of prime factorscommon multiples of 4 and 5what is the prime factorization of 28997 prime factorizationprime factors of 210the prime factorization of 140what is the prime factorization of 150prime factorization of 200composite numbers from 1 to 200greatest common factor of 35 and 36prime factorization of 240greatest prime factor of 38prime factorization 189what are common multiples of 3 and 4hcf of 72 and 9620x multiplication tablefind the prime factorization of 120prime factorization of 468greatest common factor of 64 and 48