LCM of 7 and 3


The lcm of 7 and 3 is the smallest positive integer that divides the numbers 7 and 3 without a remainder. Spelled out, it is the least common multiple of 7 and 3. Here you can find the lcm of 7 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 7 and 3, but also that of three or more integers including seven and three for example. Keep reading to learn everything about the lcm (7,3) and the terms related to it.

What is the LCM of 7 and 3

If you just want to know what is the least common multiple of 7 and 3, it is 21. Usually, this is written as

lcm(7,3) = 21

The lcm of 7 and 3 can be obtained like this:

  • The multiples of 7 are …, 14, 21, 28, ….
  • The multiples of 3 are …, 18, 21, 24, …
  • The common multiples of 7 and 3 are n x 21, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 7 ∩ multiples of 3 the least positive element is 21.
  • Therefore, the least common multiple of 7 and 3 is 21.

Taking the above into account you also know how to find all the common multiples of 7 and 3, not just the smallest. In the next section we show you how to calculate the lcm of seven and three by means of two more methods.

How to find the LCM of 7 and 3

The least common multiple of 7 and 3 can be computed by using the greatest common factor aka gcf of 7 and 3. This is the easiest approach:

lcm (7,3) = $\frac{7 \times 3}{gcf(7,3)} = \frac{21}{1}$ = 21

Alternatively, the lcm of 7 and 3 can be found using the prime factorization of 7 and 3:

  • The prime factorization of 7 is: 7
  • 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(7,7) = 21

In any case, the easiest way to compute the lcm of two numbers like 7 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 7,3. Push the button only to start over.

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

Use of LCM of 7 and 3

What is the least common multiple of 7 and 3 used for? Answer: It is helpful for adding and subtracting fractions like 1/7 and 1/3. Just multiply the dividends and divisors by 3 and 7, respectively, such that the divisors have the value of 21, the lcm of 7 and 3.

$\frac{1}{7} + \frac{1}{3} = \frac{3}{21} + \frac{7}{21} = \frac{10}{21}$. $\hspace{30px}\frac{1}{7} – \frac{1}{3} = \frac{3}{21} – \frac{7}{21} = \frac{-4}{21}$.

Properties of LCM of 7 and 3

The most important properties of the lcm(7,3) are:

  • Commutative property: lcm(7,3) = lcm(3,7)
  • Associative property: lcm(7,3,n) = lcm(lcm(3,7),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 7 and 3 is 21. In common notation: lcm (7,3) = 21.

If you have been searching for lcm 7 and 3 or lcm 7 3 then you have come to the correct page, too. The same is the true if you typed lcm for 7 and 3 in your favorite search engine.

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

Questions and comments related to the lcm of 7 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 7 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


what is the lcm of 60 and 150prime factor of 54is 117 a prime or composite numbertimes table 15x15what is the prime factorization of 462what is the prime factorization of 420common multiples of 6 and 4prime factors of 68100-74what is the prime factorization of 4845 prime factorizationcommon multiples of 16 and 18what is the greatest common factor of 72 and 96what is the lcm of 2 and 11prime factorization of 624what is the prime factorization of 65multiplication table chart up to 10060-42prime factorizations of 36gcf monomial calculatoris 63 prime or composite numberwhat is the prime factorization of 169what is the prime factorization of 560what are the common multiples of 3 and 4what is the prime factorization for 44find the prime factorization of 39lcm 5 7prime factorization of 648multiplication table 1-1000what is the prime factorization of 4207s times tableswhat is the prime factorization of 420factor tree of 66sevens times tables48 as a product of its prime factorsprime factors of 130composite numbers 1 1000what is prime factorization of 96common multiples of 7 and 3prime factor of 91what is the lcm of 2 and 1048 prime factorizationprime factorization of 93prime factorization for 200prime factorization for 72what is the prime factorization of 160prime factorization of 506prime factorization 57prime factorization of 299what is the lcm of 6 12 and 15common multiples of 3 and 6prime factorization of 1224is 143 a prime numbercommon multiples of 7prime factorization for 135multiplication chart to 25what is the lcm of 5 and 6what is the gcf of 96 48 and 84greatest common factor of 39 and 52is 221 a prime numbermultiplication table upto 30gcf of 45 and 63lcm of 63factor tree for 9615x15 multiplication tableprime factorization of 504prime factorization for 8prime factors of 315what is the prime factorization of 22570 prime factorizationfactor tree for 78is 161 a prime numberwhat is the prime factorization of 4849times tableprime factorization of 105common multiples of 6 and 12gcf of 81 and 48