LCM of 9 and 7


The lcm of 9 and 7 is the smallest positive integer that divides the numbers 9 and 7 without a remainder. Spelled out, it is the least common multiple of 9 and 7. Here you can find the lcm of 9 and 7, 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 9 and 7, but also that of three or more integers including nine and seven for example. Keep reading to learn everything about the lcm (9,7) and the terms related to it.

What is the LCM of 9 and 7

If you just want to know what is the least common multiple of 9 and 7, it is 63. Usually, this is written as

lcm(9,7) = 63

The lcm of 9 and 7 can be obtained like this:

  • The multiples of 9 are …, 54, 63, 72, ….
  • The multiples of 7 are …, 56, 63, 70, …
  • The common multiples of 9 and 7 are n x 63, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 9 ∩ multiples of 7 the least positive element is 63.
  • Therefore, the least common multiple of 9 and 7 is 63.

Taking the above into account you also know how to find all the common multiples of 9 and 7, not just the smallest. In the next section we show you how to calculate the lcm of nine and seven by means of two more methods.

How to find the LCM of 9 and 7

The least common multiple of 9 and 7 can be computed by using the greatest common factor aka gcf of 9 and 7. This is the easiest approach:

lcm (9,7) = $\frac{9 \times 7}{gcf(9,7)} = \frac{63}{1}$ = 63

Alternatively, the lcm of 9 and 7 can be found using the prime factorization of 9 and 7:

  • The prime factorization of 9 is: 3 x 3
  • The prime factorization of 7 is: 7
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(9,9) = 63

In any case, the easiest way to compute the lcm of two numbers like 9 and 7 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 9,7. Push the button only to start over.

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

Use of LCM of 9 and 7

What is the least common multiple of 9 and 7 used for? Answer: It is helpful for adding and subtracting fractions like 1/9 and 1/7. Just multiply the dividends and divisors by 7 and 9, respectively, such that the divisors have the value of 63, the lcm of 9 and 7.

$\frac{1}{9} + \frac{1}{7} = \frac{7}{63} + \frac{9}{63} = \frac{16}{63}$. $\hspace{30px}\frac{1}{9} – \frac{1}{7} = \frac{7}{63} – \frac{9}{63} = \frac{-2}{63}$.

Properties of LCM of 9 and 7

The most important properties of the lcm(9,7) are:

  • Commutative property: lcm(9,7) = lcm(7,9)
  • Associative property: lcm(9,7,n) = lcm(lcm(7,9),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 9 and 7 is 63. In common notation: lcm (9,7) = 63.

If you have been searching for lcm 9 and 7 or lcm 9 7 then you have come to the correct page, too. The same is the true if you typed lcm for 9 and 7 in your favorite search engine.

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

Questions and comments related to the lcm of 9 and 7 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 9 and 7 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


is 19 a prime or composite numberprintable multiplication chart 1-20multiplication tables upto 20 pdfwhat is the prime factorization of 138what is the lcm of 4 and 6factorization of 147multiplication tables upto 20 pdffactor tree of 9666 prime factorizationmultiplication tables 1-20what is the prime factorization of 81multiplication table 1-25what are the prime factors of 66is 179 a prime numberwhat is the prime factorization of 147the prime factorization of 147find the prime factorization of 85prime factorization of 123what is prime factorization of 48common multiples of 10what is the highest common factor of 48 and 88common multiples of 3 and 6common multiples of 3 and 9is 63 a prime number or a composite number54 prime factorizationgcf of 49 and 81what is the greatest common factor of 54 and 36what is the prime factorization of 126greatest common factor of 39 and 52prime factors of 95what is the prime factorization of 65prime factorization of 24440x40 multiplication chartprime factorization of 29499 prime factorizationmultiplication table 60x60find the gcf of 48 and 72prime factorization for 55greatest common factor of 42 and 63composite numbers to 1000factorization of 245prime factorization for 44common multiples of 6is 147 a prime numberwhat is the lcm of 2 and 5prime factorization for 200gcf of 81 and 36what is the gcf of 34 and 85what is the prime factorization of 360prime factorization of 58what is the prime factorization of 1356s times tablesprime factors of 440multiplication table 1-16prime factorization 57what is the prime factorization of 330prime factorization for 54lcm of 144gcf methodprime factorization of 378largest common denominator calculatorthe prime factorization of 121is 125 a prime or composite numberprime factorization of 108greatest common factor of 48 and 54multiplication table up to 1000is 162 a prime number132 prime factorizationprime factorization for 200multiplication table 40x40what is the prime factorization for 180what is the prime factorization of 294what is the greatest common factor of 72 and 96is 30 a prime or composite number