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LCM of 82 and 3

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The lcm of 82 and 3 is the smallest positive integer that divides the numbers 82 and 3 without a remainder. Spelled out, it is the least common multiple of 82 and 3. Here you can find the lcm of 82 and 3, 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 82 and 3, but also that of three or more integers including eighty-two and three for example. Keep reading to learn everything about the lcm (82,3) and the terms related to it.

What is the LCM of 82 and 3

If you just want to know what is the least common multiple of 82 and 3, it is 246. Usually, this is written as

lcm(82,3) = 246

The lcm of 82 and 3 can be obtained like this:

  • The multiples of 82 are … , 164, 246, 328, ….
  • The multiples of 3 are …, 243, 246, 249, …
  • The common multiples of 82 and 3 are n x 246, intersecting the two sets above, n\neq 0 \thinspace\in\thinspace\mathbb{Z}.
  • In the intersection multiples of 82 ∩ multiples of 3 the least positive element is 246.
  • Therefore, the least common multiple of 82 and 3 is 246.

Taking the above into account you also know how to find all the common multiples of 82 and 3, not just the smallest. In the next section we show you how to calculate the lcm of eighty-two and three by means of two more methods.

How to find the LCM of 82 and 3

The least common multiple of 82 and 3 can be computed by using the greatest common factor aka gcf of 82 and 3. This is the easiest approach:

lcm (82,3) = \frac{82 \times 3}{gcf(82,3)} = \frac{246}{1} = 246

Alternatively, the lcm of 82 and 3 can be found using the prime factorization of 82 and 3:

  • The prime factorization of 82 is: 2 x 41
  • The prime factorization of 3 is: 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) = 246

In any case, the easiest way to compute the lcm of two numbers like 82 and 3 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 82,3. Push the button only to start over.

The lcm is...
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Use of LCM of 82 and 3

What is the least common multiple of 82 and 3 used for? Answer: It is helpful for adding and subtracting fractions like 1/82 and 1/3. Just multiply the dividends and divisors by 3 and 82, respectively, such that the divisors have the value of 246, the lcm of 82 and 3.

\frac{1}{82} + \frac{1}{3} = \frac{3}{246} + \frac{82}{246} = \frac{85}{246}. \frac{1}{82} - \frac{1}{3} = \frac{3}{246} - \frac{82}{246} = \frac{-79}{246}.

Properties of LCM of 82 and 3

The most important properties of the lcm(82,3) are:

  • Commutative property: lcm(82,3) = lcm(3,82)
  • Associative property: lcm(82,3,n) = lcm(lcm(3,82),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 82 and 3 is 246. In common notation: lcm (82,3) = 246.

If you have been searching for lcm 82 and 3 or lcm 82 3 then you have come to the correct page, too. The same is the true if you typed lcm for 82 and 3 in your favorite search engine.

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

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