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.
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
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:
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.
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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.
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