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The lcm of 42 and 27 is the smallest positive integer that divides the numbers 42 and 27 without a remainder. Spelled out, it is the least common multiple of 42 and 27. Here you can find the result for 42 and 27, along with a total of three methods for computing it.
378
What is the Least Common Multiple of 42 and 27?
If you just want to know what is the least common multiple of 42 and 27, it is 378. Usually, this is written as
The lcm of 42 and 27 can be obtained like this:
- The multiples of 42 are … , 336, 378, 420, ….
- The multiples of 27 are …, 351, 378, 405, …
- The common multiples of 42 and 27 are n x 378, intersecting the two sets above,
. - In the intersection multiples of 42 ∩ multiples of 27 the least positive element is 378.
- Therefore, the least common multiple of 42 and 27 is 378.
Taking the above into account you also know how to find all the common multiples of 42 and 27, not just the smallest. In the next section we show you how to calculate the lcm of forty-two and twenty-seven by means of two more methods.
How to find the LCM of 42 and 27
The least common multiple of 42 and 27 can be computed by using the greatest common factor aka gcf of 42 and 27. This is the easiest approach:
Alternatively, the lcm of 42 and 27 can be found using the prime factorization of 42 and 27:
- The prime factorization of 42 is: 2 x 3 x 7
- The prime factorization of 27 is: 3 x 3 x 3
- Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(42,42) = 378
In any case, the easiest way to compute the result for two numbers like 42 and 27 is by using our calculator above. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 42,272,2. Push the button only to start over.
Similar searched terms on our site also include:
In the next paragraph we explain how the mathematical concept can be employed.
Keep reading – it’s really interesting.
Use of Least Common Multiple of 42 and 27
What is the least common multiple of 42 and 27 used for? Answer: It is helpful for adding and subtracting fractions like 1/42 and 1/27. Just multiply the dividends and divisors by 9 and 14, respectively, such that the divisors have the value of 378, the lcm of 42 and 27.
Next, we shed a light on the mathematical properties.
Properties of LCM of 42 and 27
The most important properties of the lcm(42,27) are:
- Commutative property: lcm(42,27) = lcm(27,42)
- Associative property: lcm(42,27,n) = lcm(lcm(27,42),n)
The associativity is particularly useful to get the lcm of three or more numbers; our calculator makes use of it.
Summary
Note that you can find the least common multiple of many integer pairs including forty-two / twenty-seven by using the search form in the sidebar of this page.
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– Article written by Mark, last updated on August 8th, 2023