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The lcm of 91 and 31 is the smallest positive integer that divides the numbers 91 and 31 without a remainder. Spelled out, it is the least common multiple of 91 and 31. Here you can find the lcm of 91 and 31, along with a total of three methods for computing it.
What is the LCM of 91 and 31
If you just want to know what is the least common multiple of 91 and 31, it is 2821. Usually, this is written as
The lcm of 91 and 31 can be obtained like this:
- The multiples of 91 are … , 2730, 2821, 2912, ….
- The multiples of 31 are …, 2790, 2821, 2852, …
- The common multiples of 91 and 31 are n x 2821, intersecting the two sets above,
- In the intersection multiples of 91 ∩ multiples of 31 the least positive element is 2821.
- Therefore, the least common multiple of 91 and 31 is 2821.
Taking the above into account you also know how to find all the common multiples of 91 and 31, not just the smallest. In the next section we show you how to calculate the lcm of ninety-one and thirty-one by means of two more methods.
How to find the LCM of 91 and 31
The least common multiple of 91 and 31 can be computed by using the greatest common factor aka gcf of 91 and 31. This is the easiest approach:
Alternatively, the lcm of 91 and 31 can be found using the prime factorization of 91 and 31:
- The prime factorization of 91 is: 7 x 13
- The prime factorization of 31 is: 31
- Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(91,91) = 2821
In any case, the easiest way to compute the lcm of two numbers like 91 and 31 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 91,31. Push the button only to start over.
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Use of LCM of 91 and 31
What is the least common multiple of 91 and 31 used for? Answer: It is helpful for adding and subtracting fractions like 1/91 and 1/31. Just multiply the dividends and divisors by 31 and 91, respectively, such that the divisors have the value of 2821, the lcm of 91 and 31.
Properties of LCM of 91 and 31
The most important properties of the lcm(91,31) are:
- Commutative property: lcm(91,31) = lcm(31,91)
- Associative property: lcm(91,31,n) = lcm(lcm(31,91),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 91 and 31 is 2821. In common notation: lcm (91,31) = 2821.
If you have been searching for lcm 91 and 31 or lcm 91 31 then you have come to the correct page, too. The same is the true if you typed lcm for 91 and 31 in your favorite search engine.
Note that you can find the least common multiple of many integer pairs including ninety-one / thirty-one by using the search form in the sidebar of this page.
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