The lcm of 6 and 83 is the smallest positive integer that divides the numbers 6 and 83 without a remainder. Spelled out, it is the least common multiple of 6 and 83. Here you can find the lcm of 6 and 83, along with a total of three methods for computing it.
What is the LCM of 6 and 83
If you just want to know what is the least common multiple of 6 and 83, it is 498. Usually, this is written as
The lcm of 6 and 83 can be obtained like this:
- The multiples of 6 are … , 492, 498, 504, ….
- The multiples of 83 are …, 415, 498, 581, …
- The common multiples of 6 and 83 are n x 498, intersecting the two sets above,
- In the intersection multiples of 6 ∩ multiples of 83 the least positive element is 498.
- Therefore, the least common multiple of 6 and 83 is 498.
Taking the above into account you also know how to find all the common multiples of 6 and 83, not just the smallest. In the next section we show you how to calculate the lcm of six and eighty-three by means of two more methods.
How to find the LCM of 6 and 83
The least common multiple of 6 and 83 can be computed by using the greatest common factor aka gcf of 6 and 83. This is the easiest approach:
Alternatively, the lcm of 6 and 83 can be found using the prime factorization of 6 and 83:
- The prime factorization of 6 is: 2 x 3
- The prime factorization of 83 is: 83
- Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(6,6) = 498
In any case, the easiest way to compute the lcm of two numbers like 6 and 83 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 6,83. Push the button only to start over.
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Use of LCM of 6 and 83
What is the least common multiple of 6 and 83 used for? Answer: It is helpful for adding and subtracting fractions like 1/6 and 1/83. Just multiply the dividends and divisors by 83 and 6, respectively, such that the divisors have the value of 498, the lcm of 6 and 83.
Properties of LCM of 6 and 83
The most important properties of the lcm(6,83) are:
- Commutative property: lcm(6,83) = lcm(83,6)
- Associative property: lcm(6,83,n) = lcm(lcm(83,6),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 83 is 498. In common notation: lcm (6,83) = 498.
If you have been searching for lcm 6 and 83 or lcm 6 83 then you have come to the correct page, too. The same is the true if you typed lcm for 6 and 83 in your favorite search engine.
Note that you can find the least common multiple of many integer pairs including six / eighty-three by using the search form in the sidebar of this page.
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