Home » Least Common Multiple » LCM of 6 and 84

# LCM of 6 and 84

The lcm of 6 and 84 is the smallest positive integer that divides the numbers 6 and 84 without a remainder. Spelled out, it is the least common multiple of 6 and 84. Here you can find the lcm of 6 and 84, along with a total of three methods for computing it.

84

In addition, we have a calculator you should check out. Not only can it determine the lcm of 6 and 84, but also that of three or more integers including six and eighty-four for example. Keep reading to learn everything about the lcm (6,84) and the terms related to it.

## What is the LCM of 6 and 84

If you just want to know what is the least common multiple of 6 and 84, it is 84. Usually, this is written as

lcm(6,84) = 84

The lcm of 6 and 84 can be obtained like this:

• The multiples of 6 are … , 78, 84, 90, ….
• The multiples of 84 are …, 0, 84, 168, …
• The common multiples of 6 and 84 are n x 84, intersecting the two sets above, .
• In the intersection multiples of 6 ∩ multiples of 84 the least positive element is 84.
• Therefore, the least common multiple of 6 and 84 is 84.

Taking the above into account you also know how to find all the common multiples of 6 and 84, not just the smallest. In the next section we show you how to calculate the lcm of six and eighty-four by means of two more methods.

## How to find the LCM of 6 and 84

The least common multiple of 6 and 84 can be computed by using the greatest common factor aka gcf of 6 and 84. This is the easiest approach:

lcm (6,84) = = 84

Alternatively, the lcm of 6 and 84 can be found using the prime factorization of 6 and 84:

• The prime factorization of 6 is: 2 x 3
• The prime factorization of 84 is: 2 x 2 x 3 x 7
• Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(6,6) = 84

In any case, the easiest way to compute the lcm of two numbers like 6 and 84 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 6,84. Push the button only to start over.

Similar searched terms on our site also include:

## Use of LCM of 6 and 84

What is the least common multiple of 6 and 84 used for? Answer: It is helpful for adding and subtracting fractions like 1/6 and 1/84. Just multiply the dividends and divisors by 14 and 1, respectively, such that the divisors have the value of 84, the lcm of 6 and 84.

. .

## Properties of LCM of 6 and 84

The most important properties of the lcm(6,84) are:

• Commutative property: lcm(6,84) = lcm(84,6)
• Associative property: lcm(6,84,n) = lcm(lcm(84,6),n)

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 6 and 84 is 84. In common notation: lcm (6,84) = 84.

If you have been searching for lcm 6 and 84 or lcm 6 84 then you have come to the correct page, too. The same is the true if you typed lcm for 6 and 84 in your favorite search engine.

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

Questions and comments related to the lcm of 6 and 84 are really appreciated. Use the form below or send us a mail to get in touch.

Please hit the sharing buttons if our article about the least common multiple of 6 and 84 has been useful to you, and make sure to bookmark our site.