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LCM of 78 and 51

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The lcm of 78 and 51 is the smallest positive integer that divides the numbers 78 and 51 without a remainder. Spelled out, it is the least common multiple of 78 and 51. Here you can find the lcm of 78 and 51, 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 78 and 51, but also that of three or more integers including seventy-eight and fifty-one for example. Keep reading to learn everything about the lcm (78,51) and the terms related to it.

What is the LCM of 78 and 51

If you just want to know what is the least common multiple of 78 and 51, it is 1326. Usually, this is written as

lcm(78,51) = 1326

The lcm of 78 and 51 can be obtained like this:

  • The multiples of 78 are … , 1248, 1326, 1404, ….
  • The multiples of 51 are …, 1275, 1326, 1377, …
  • The common multiples of 78 and 51 are n x 1326, intersecting the two sets above, n\neq 0 \thinspace\in\thinspace\mathbb{Z}.
  • In the intersection multiples of 78 ∩ multiples of 51 the least positive element is 1326.
  • Therefore, the least common multiple of 78 and 51 is 1326.

Taking the above into account you also know how to find all the common multiples of 78 and 51, not just the smallest. In the next section we show you how to calculate the lcm of seventy-eight and fifty-one by means of two more methods.

How to find the LCM of 78 and 51

The least common multiple of 78 and 51 can be computed by using the greatest common factor aka gcf of 78 and 51. This is the easiest approach:

lcm (78,51) = \frac{78 \times 51}{gcf(78,51)} = \frac{3978}{3} = 1326

Alternatively, the lcm of 78 and 51 can be found using the prime factorization of 78 and 51:

  • The prime factorization of 78 is: 2 x 3 x 13
  • The prime factorization of 51 is: 3 x 17
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(78,78) = 1326

In any case, the easiest way to compute the lcm of two numbers like 78 and 51 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 78,51. Push the button only to start over.

The lcm is...
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Use of LCM of 78 and 51

What is the least common multiple of 78 and 51 used for? Answer: It is helpful for adding and subtracting fractions like 1/78 and 1/51. Just multiply the dividends and divisors by 17 and 26, respectively, such that the divisors have the value of 1326, the lcm of 78 and 51.

\frac{1}{78} + \frac{1}{51} = \frac{17}{1326} + \frac{26}{1326} = \frac{43}{1326}. \frac{1}{78} - \frac{1}{51} = \frac{17}{1326} - \frac{26}{1326} = \frac{-9}{1326}.

Properties of LCM of 78 and 51

The most important properties of the lcm(78,51) are:

  • Commutative property: lcm(78,51) = lcm(51,78)
  • Associative property: lcm(78,51,n) = lcm(lcm(51,78),n) n\neq 0 \thinspace\in\thinspace\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 78 and 51 is 1326. In common notation: lcm (78,51) = 1326.

If you have been searching for lcm 78 and 51 or lcm 78 51 then you have come to the correct page, too. The same is the true if you typed lcm for 78 and 51 in your favorite search engine.

Note that you can find the least common multiple of many integer pairs including seventy-eight / fifty-one by using the search form in the sidebar of this page.

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