LCM of 39 and 86


The lcm of 39 and 86 is the smallest positive integer that divides the numbers 39 and 86 without a remainder. Spelled out, it is the least common multiple of 39 and 86. Here you can find the lcm of 39 and 86, 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 39 and 86, but also that of three or more integers including thirty-nine and eighty-six for example. Keep reading to learn everything about the lcm (39,86) and the terms related to it.

What is the LCM of 39 and 86

If you just want to know what is the least common multiple of 39 and 86, it is 3354. Usually, this is written as

lcm(39,86) = 3354

The lcm of 39 and 86 can be obtained like this:

  • The multiples of 39 are … , 3315, 3354, 3393, ….
  • The multiples of 86 are …, 3268, 3354, 3440, …
  • The common multiples of 39 and 86 are n x 3354, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 39 ∩ multiples of 86 the least positive element is 3354.
  • Therefore, the least common multiple of 39 and 86 is 3354.

Taking the above into account you also know how to find all the common multiples of 39 and 86, not just the smallest. In the next section we show you how to calculate the lcm of thirty-nine and eighty-six by means of two more methods.

How to find the LCM of 39 and 86

The least common multiple of 39 and 86 can be computed by using the greatest common factor aka gcf of 39 and 86. This is the easiest approach:

lcm (39,86) = $\frac{39 \times 86}{gcf(39,86)} = \frac{3354}{1}$ = 3354

Alternatively, the lcm of 39 and 86 can be found using the prime factorization of 39 and 86:

  • The prime factorization of 39 is: 3 x 13
  • The prime factorization of 86 is: 2 x 43
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(39,39) = 3354

In any case, the easiest way to compute the lcm of two numbers like 39 and 86 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 39,86. Push the button only to start over.

The lcm is...
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Use of LCM of 39 and 86

What is the least common multiple of 39 and 86 used for? Answer: It is helpful for adding and subtracting fractions like 1/39 and 1/86. Just multiply the dividends and divisors by 86 and 39, respectively, such that the divisors have the value of 3354, the lcm of 39 and 86.

$\frac{1}{39} + \frac{1}{86} = \frac{86}{3354} + \frac{39}{3354} = \frac{125}{3354}$. $\hspace{30px}\frac{1}{39} – \frac{1}{86} = \frac{86}{3354} – \frac{39}{3354} = \frac{47}{3354}$.

Properties of LCM of 39 and 86

The most important properties of the lcm(39,86) are:

  • Commutative property: lcm(39,86) = lcm(86,39)
  • Associative property: lcm(39,86,n) = lcm(lcm(86,39),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 39 and 86 is 3354. In common notation: lcm (39,86) = 3354.

If you have been searching for lcm 39 and 86 or lcm 39 86 then you have come to the correct page, too. The same is the true if you typed lcm for 39 and 86 in your favorite search engine.

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

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