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LCM of 9 and 35

The lcm of 9 and 35 is the smallest positive integer that divides the numbers 9 and 35 without a remainder. Spelled out, it is the least common multiple of 9 and 35. Here you can find the result for 9 and 35, along with a total of three methods for computing it.


315

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 9 and 35, but also that of three or more integers including nine and thirty-five for example. Keep reading to learn everything about the lcm (9,35) and the terms related to it.

What is the Least Common Multiple of 9 and 35?

If you just want to know what is the least common multiple of 9 and 35, it is 315. Usually, this is written as

lcm(9,35) = 315


The lcm of 9 and 35 can be obtained like this:
  • The multiples of 9 are … , 306, 315, 324, ….
  • The multiples of 35 are …, 280, 315, 350, …
  • The common multiples of 9 and 35 are n x 315, intersecting the two sets above, .
  • In the intersection multiples of 9 ∩ multiples of 35 the least positive element is 315.
  • Therefore, the least common multiple of 9 and 35 is 315.

Taking the above into account you also know how to find all the common multiples of 9 and 35, not just the smallest. In the next section we show you how to calculate the lcm of nine and thirty-five by means of two more methods.

How to find the LCM of 9 and 35

The least common multiple of 9 and 35 can be computed by using the greatest common factor aka gcf of 9 and 35. This is the easiest approach:

lcm (9,35) = = 315



Alternatively, the lcm of 9 and 35 can be found using the prime factorization of 9 and 35:
  • The prime factorization of 9 is: 3 x 3
  • The prime factorization of 35 is: 5 x 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) = 315

In any case, the easiest way to compute the result for two numbers like 9 and 35 is by using our calculator above. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 9,352,2. Push the button only to start over.

Similar searched terms on our site also include:

In the next paragraph we explain how the mathematical concept can be employed.

Keep reading – it’s really interesting.

Use of Least Common Multiple of 9 and 35

What is the least common multiple of 9 and 35 used for? Answer: It is helpful for adding and subtracting fractions like 1/9 and 1/35. Just multiply the dividends and divisors by 35 and 9, respectively, such that the divisors have the value of 315, the lcm of 9 and 35.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 9 and 35

The most important properties of the lcm(9,35) are:

  • Commutative property: lcm(9,35) = lcm(35,9)
  • Associative property: lcm(9,35,n) = lcm(lcm(35,9),n)

The associativity is particularly useful to get the lcm of three or more numbers; our calculator makes use of it.

Summary

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

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– Article written by Mark, last updated on August 8th, 2023