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LCM of 78 and 56

The lcm of 78 and 56 is the smallest positive integer that divides the numbers 78 and 56 without a remainder. Spelled out, it is the least common multiple of 78 and 56. Here you can find the result for 78 and 56, along with a total of three methods for computing it.


2184

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 78 and 56, but also that of three or more integers including seventy-eight and fifty-six for example. Keep reading to learn everything about the lcm (78,56) and the terms related to it.

What is the Least Common Multiple of 78 and 56?

If you just want to know what is the least common multiple of 78 and 56, it is 2184. Usually, this is written as

lcm(78,56) = 2184


The lcm of 78 and 56 can be obtained like this:
  • The multiples of 78 are … , 2106, 2184, 2262, ….
  • The multiples of 56 are …, 2128, 2184, 2240, …
  • The common multiples of 78 and 56 are n x 2184, intersecting the two sets above, .
  • In the intersection multiples of 78 ∩ multiples of 56 the least positive element is 2184.
  • Therefore, the least common multiple of 78 and 56 is 2184.

Taking the above into account you also know how to find all the common multiples of 78 and 56, not just the smallest. In the next section we show you how to calculate the lcm of seventy-eight and fifty-six by means of two more methods.

How to find the LCM of 78 and 56

The least common multiple of 78 and 56 can be computed by using the greatest common factor aka gcf of 78 and 56. This is the easiest approach:

lcm (78,56) = = 2184



Alternatively, the lcm of 78 and 56 can be found using the prime factorization of 78 and 56:
  • The prime factorization of 78 is: 2 x 3 x 13
  • The prime factorization of 56 is: 2 x 2 x 2 x 7
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(78,78) = 2184

In any case, the easiest way to compute the result for two numbers like 78 and 56 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 78,562,2. 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 78 and 56

What is the least common multiple of 78 and 56 used for? Answer: It is helpful for adding and subtracting fractions like 1/78 and 1/56. Just multiply the dividends and divisors by 28 and 39, respectively, such that the divisors have the value of 2184, the lcm of 78 and 56.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 78 and 56

The most important properties of the lcm(78,56) are:

  • Commutative property: lcm(78,56) = lcm(56,78)
  • Associative property: lcm(78,56,n) = lcm(lcm(56,78),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 seventy-eight / fifty-six 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