LCM of 2 and 3


The lcm of 2 and 3 is the smallest positive integer that divides the numbers 2 and 3 without a remainder. Spelled out, it is the least common multiple of 2 and 3. Here you can find the lcm of 2 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 2 and 3, but also that of three or more integers including two and three for example. Keep reading to learn everything about the lcm (2,3) and the terms related to it.

What is the LCM of 2 and 3

If you just want to know what is the least common multiple of 2 and 3, it is 6. Usually, this is written as

lcm(2,3) = 6

The lcm of 2 and 3 can be obtained like this:

  • The multiples of 2 are …, 4, 6, 8, ….
  • The multiples of 3 are …, 3, 6, 9, …
  • The common multiples of 2 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 2 ∩ multiples of 3 the least positive element is 6.
  • Therefore, the least common multiple of 2 and 3 is 6.

Taking the above into account you also know how to find all the common multiples of 2 and 3, not just the smallest. In the next section we show you how to calculate the lcm of two and three by means of two more methods.

How to find the LCM of 2 and 3

The least common multiple of 2 and 3 can be computed by using the greatest common factor aka gcf of 2 and 3. This is the easiest approach:

lcm (2,3) = $\frac{2 \times 3}{gcf(2,3)} = \frac{6}{1}$ = 6

Alternatively, the lcm of 2 and 3 can be found using the prime factorization of 2 and 3:

  • The prime factorization of 2 is: 2
  • 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(2,2) = 6

In any case, the easiest way to compute the lcm of two numbers like 2 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 2,3. Push the button only to start over.

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

Use of LCM of 2 and 3

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

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

Properties of LCM of 2 and 3

The most important properties of the lcm(2,3) are:

  • Commutative property: lcm(2,3) = lcm(3,2)
  • Associative property: lcm(2,3,n) = lcm(lcm(3,2),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 2 and 3 is 6. In common notation: lcm (2,3) = 6.

If you have been searching for lcm 2 and 3 or lcm 2 3 then you have come to the correct page, too. The same is the true if you typed lcm for 2 and 3 in your favorite search engine.

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

Questions and comments related to the lcm of 2 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 2 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


8x tableswrite the prime factorization of 72whats gcf45 prime factorizationis 87 a prime or composite numberprime factor of 112what is the prime factorization of 221prime factors of 330prime factorization of 160multiplication chart up to 10000what is the lcm of 2 and 8what is the prime factorization for 200gcf of 45 and 75what is the greatest common factor of 34 and 51gcf of 56 and 6370 prime factorizationgcfcalculatorprime factorization of 190prime factorization 180prime factorization of 728determine the prime factorization of 88gcf calculatergcf of 121multiplication table 20x20 printable84 as a product of prime factorswhat is the gcf of 63 and 42what is the greatest common factor of 42 and 70gcf of 69 and 92what is the prime factorization of 175what is the gcf of 96 48 and 84144 prime factorizationis 197 a prime numberprime factorization of 650prime factorizations of 36what is the lcm of 2 and 8what is 42 as a product of prime factorswrite 600 as a product of its prime factorsis 179 a prime numberwhat is the prime factorization of 1000prime factorization of 312greatest common factor of 120what is the prime factorization for 56what is the lcm of 1540x timetablewhat is the prime factorization of 1000prime factors for 54prime factorization of 343what is the lcm of 10 and 5express 126 as a product of prime numbersfind the prime factorization of 85prime factorization of 38greatest common factor of 36 and 4412 x 12 multiplication tablegcf of 96 and 144what is the prime factorization of 201greatest prime factor of 6884 prime factorization36-27-36common multiples of 10 and 15what is the gcf of 35 and 63find the prime factorization of 52prime factorization 98what is the lcm of 12divisors of 75prime factorization of 300prime factor of 108common multiples of 8 and 10what is the greatest common factor of 54 and 63lcm of 63what is the gcf of 33 and 66what is the greatest common factor of 32 and 56multiplication chart 1-9is 113 a prime numbergcf and lcm finder84-35multiplication table 1-100 printablemultiplication chart up to 200gcf of 147what is the greatest common factor of 60 and 72prime factorization of 300