LCM of 3 and 6


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

What is the LCM of 3 and 6

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

lcm(3,6) = 6

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

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

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

How to find the LCM of 3 and 6

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

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

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

  • The prime factorization of 3 is: 3
  • 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(3,3) = 6

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

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

Use of LCM of 3 and 6

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

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

Properties of LCM of 3 and 6

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

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

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

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

Questions and comments related to the lcm of 3 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 3 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


prime factorization of 770what is the prime factorization of 264multiplication table 1-20 printableprime factorization of 190common multiples of 4 and 9what is the prime factorization of 14249 prime factorizationgcf calculaterprime factors of 293greatest common factor of 28 and 44prime factorization of 95prime factorization of 41prime factors 72gcf of 56 and 63lcm of 18 and 72prime factorization of 40542 prime factorizationthe prime factorization of 245is 117 a prime or composite numberprime factors of 250prime factorization for 1000what is the least common multiple of 48 and 72what is the factor tree of 63what is the prime factorization of 180what is the prime factorization of 2800greatest common factor of 54 and 72multiplication table to 40multiplication table 25x25 printablegcf and lcm of 36 and 45is 86 a prime or composite numberlcm of 63is 121 prime numberprime factorization of 405prime factorization of 138the prime factorization of 343is 197 a prime numberis 983 a prime numbercommon multiples of 4 and 5common multiples for 8 and 12common denominator of 5 and 8multiplication chart 30x30is 27 a prime number or a composite numberwhat are the prime factorization of 44multiplication chart 1-100what is the prime factorization of 99225 prime factorizationfactor tree for 144highest common factor calculator 3 numbersis 19 a prime or composite numberis 68 a prime or composite numberwhat is the prime factorization of 315prime factorization 99what is the prime factorization of 58multiplication chart that goes to 100prime factorization of 561prime factorization of 47find the greatest common factor calculatorwhat is the greatest common factor of 35 and 49divisors of 75what is the lcm of 3 and 4write 99 as a product of prime factorswhat is the gcf of 32 and 64prime factorization of 440what are the prime factors of 65prime factorization of 1900prime factorization for 104is 72 a prime or composite numberprime factorization of 266multiplication table 1-13is 199 a prime numbermultiplication chart that goes up to 20find the prime factorization of 40write 42 as a product of prime factors101 prime factorizationmultiplication table that goes up to 20