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


gcf calculaterwhat is the prime factorization of 4825x25 multiplication chart702 756 5346gcf of 98prime factorization of 294prime factorization of 344multiplication table of 42what is the prime factorization of 285the prime factorization of 10551 prime factorizationprime factorization of 192common multiples of 4 and 9whats a prime factorprime factorization of 918s times tableswhat is the gcf of 48 and 64multiplication chart to 300greatest common factor chartprime factorization 360common multiples of 3 and 6prime factorization 88prime factorization of 169prime factorization of 450gcf and lcm of 36 and 45what is the prime factorization of 80common multiples of 15what is the greatest common factor of 54 and 36prime factorization of 220common multiples of 4 and 9is 147 a prime numbergcf of 32 and 7263 prime factorizationgcf of 28 and 42multiplication table chart up to 100what is the lcm of 6prime factorisation of 47what is the prime factorization of 540what is the prime factorization of 425what is prime factorization of 48calculator for gcf100-68what is 36 as a product of prime factorsthe prime factorization of 300is 91 a prime or composite numberprime factorization for 105common denominator of 5 and 10what are the prime factors of 102multiplication 5 times tableswhat is the prime factorization of 735write 98 as a product of prime factorsprime factors of 92greatest common factor of 54 and 36greatest common factor of 64 and 80what is the prime factorization of 150prime factorization of 210prime factorization for 75what is the prime factorization of 450prime factor of 52find the prime factorization of 42highest common denominator calculatordefine prime factorisation100-85prime factorization of 154prime factorization 180what is the greatest common factor of 54 and 36prime factors of 293multiplication table 1-20prime numbers 1-60list of prime factors 1 1000factorization of 245gcf of 75 and 90prime factorization of 195composite numbers 1-200