The lcm of 82 and 46 is the smallest positive integer that divides the numbers 82 and 46 without a remainder. Spelled out, it is the least common multiple of 82 and 46. Here you can find the lcm of 82 and 46, along with a total of three methods for computing it.
What is the LCM of 82 and 46
If you just want to know what is the least common multiple of 82 and 46, it is 1886. Usually, this is written as
The lcm of 82 and 46 can be obtained like this:
- The multiples of 82 are … , 1804, 1886, 1968, ….
- The multiples of 46 are …, 1840, 1886, 1932, …
- The common multiples of 82 and 46 are n x 1886, intersecting the two sets above,
- In the intersection multiples of 82 ∩ multiples of 46 the least positive element is 1886.
- Therefore, the least common multiple of 82 and 46 is 1886.
Taking the above into account you also know how to find all the common multiples of 82 and 46, not just the smallest. In the next section we show you how to calculate the lcm of eighty-two and forty-six by means of two more methods.
How to find the LCM of 82 and 46
The least common multiple of 82 and 46 can be computed by using the greatest common factor aka gcf of 82 and 46. This is the easiest approach:
Alternatively, the lcm of 82 and 46 can be found using the prime factorization of 82 and 46:
- The prime factorization of 82 is: 2 x 41
- The prime factorization of 46 is: 2 x 23
- Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(82,82) = 1886
In any case, the easiest way to compute the lcm of two numbers like 82 and 46 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 82,46. Push the button only to start over.
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Use of LCM of 82 and 46
What is the least common multiple of 82 and 46 used for? Answer: It is helpful for adding and subtracting fractions like 1/82 and 1/46. Just multiply the dividends and divisors by 23 and 41, respectively, such that the divisors have the value of 1886, the lcm of 82 and 46.
Properties of LCM of 82 and 46
The most important properties of the lcm(82,46) are:
- Commutative property: lcm(82,46) = lcm(46,82)
- Associative property: lcm(82,46,n) = lcm(lcm(46,82),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 82 and 46 is 1886. In common notation: lcm (82,46) = 1886.
If you have been searching for lcm 82 and 46 or lcm 82 46 then you have come to the correct page, too. The same is the true if you typed lcm for 82 and 46 in your favorite search engine.
Note that you can find the least common multiple of many integer pairs including eighty-two / forty-six by using the search form in the sidebar of this page.
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