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LCM of 82 and 9

The lcm of 82 and 9 is the smallest positive integer that divides the numbers 82 and 9 without a remainder. Spelled out, it is the least common multiple of 82 and 9. Here you can find the result for 82 and 9, along with a total of three methods for computing it.


738

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 82 and 9, but also that of three or more integers including eighty-two and nine for example. Keep reading to learn everything about the lcm (82,9) and the terms related to it.

What is the Least Common Multiple of 82 and 9?

If you just want to know what is the least common multiple of 82 and 9, it is 738. Usually, this is written as

lcm(82,9) = 738


The lcm of 82 and 9 can be obtained like this:
  • The multiples of 82 are … , 656, 738, 820, ….
  • The multiples of 9 are …, 729, 738, 747, …
  • The common multiples of 82 and 9 are n x 738, intersecting the two sets above, .
  • In the intersection multiples of 82 ∩ multiples of 9 the least positive element is 738.
  • Therefore, the least common multiple of 82 and 9 is 738.

Taking the above into account you also know how to find all the common multiples of 82 and 9, not just the smallest. In the next section we show you how to calculate the lcm of eighty-two and nine by means of two more methods.

How to find the LCM of 82 and 9

The least common multiple of 82 and 9 can be computed by using the greatest common factor aka gcf of 82 and 9. This is the easiest approach:

lcm (82,9) = = 738



Alternatively, the lcm of 82 and 9 can be found using the prime factorization of 82 and 9:
  • The prime factorization of 82 is: 2 x 41
  • The prime factorization of 9 is: 3 x 3
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(82,82) = 738

In any case, the easiest way to compute the result for two numbers like 82 and 9 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 82,92,2. 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 82 and 9

What is the least common multiple of 82 and 9 used for? Answer: It is helpful for adding and subtracting fractions like 1/82 and 1/9. Just multiply the dividends and divisors by 9 and 82, respectively, such that the divisors have the value of 738, the lcm of 82 and 9.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 82 and 9

The most important properties of the lcm(82,9) are:

  • Commutative property: lcm(82,9) = lcm(9,82)
  • Associative property: lcm(82,9,n) = lcm(lcm(9,82),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 eighty-two / nine 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