The lcm of 87 and 48 is the smallest positive integer that divides the numbers 87 and 48 without a remainder. Spelled out, it is the least common multiple of 87 and 48. Here you can find the lcm of 87 and 48, along with a total of three methods for computing it.
What is the LCM of 87 and 48
If you just want to know what is the least common multiple of 87 and 48, it is 1392. Usually, this is written as
The lcm of 87 and 48 can be obtained like this:
- The multiples of 87 are … , 1305, 1392, 1479, ….
- The multiples of 48 are …, 1344, 1392, 1440, …
- The common multiples of 87 and 48 are n x 1392, intersecting the two sets above,
- In the intersection multiples of 87 ∩ multiples of 48 the least positive element is 1392.
- Therefore, the least common multiple of 87 and 48 is 1392.
Taking the above into account you also know how to find all the common multiples of 87 and 48, not just the smallest. In the next section we show you how to calculate the lcm of eighty-seven and forty-eight by means of two more methods.
How to find the LCM of 87 and 48
The least common multiple of 87 and 48 can be computed by using the greatest common factor aka gcf of 87 and 48. This is the easiest approach:
Alternatively, the lcm of 87 and 48 can be found using the prime factorization of 87 and 48:
- The prime factorization of 87 is: 3 x 29
- The prime factorization of 48 is: 2 x 2 x 2 x 2 x 3
- Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(87,87) = 1392
In any case, the easiest way to compute the lcm of two numbers like 87 and 48 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 87,48. Push the button only to start over.
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Use of LCM of 87 and 48
What is the least common multiple of 87 and 48 used for? Answer: It is helpful for adding and subtracting fractions like 1/87 and 1/48. Just multiply the dividends and divisors by 16 and 29, respectively, such that the divisors have the value of 1392, the lcm of 87 and 48.
Properties of LCM of 87 and 48
The most important properties of the lcm(87,48) are:
- Commutative property: lcm(87,48) = lcm(48,87)
- Associative property: lcm(87,48,n) = lcm(lcm(48,87),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 87 and 48 is 1392. In common notation: lcm (87,48) = 1392.
If you have been searching for lcm 87 and 48 or lcm 87 48 then you have come to the correct page, too. The same is the true if you typed lcm for 87 and 48 in your favorite search engine.
Note that you can find the least common multiple of many integer pairs including eighty-seven / forty-eight by using the search form in the sidebar of this page.
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