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The lcm of 39 and 14 is the smallest positive integer that divides the numbers 39 and 14 without a remainder. Spelled out, it is the least common multiple of 39 and 14. Here you can find the lcm of 39 and 14, along with a total of three methods for computing it.
What is the LCM of 39 and 14
If you just want to know what is the least common multiple of 39 and 14, it is 546. Usually, this is written as
The lcm of 39 and 14 can be obtained like this:
- The multiples of 39 are … , 507, 546, 585, ….
- The multiples of 14 are …, 532, 546, 560, …
- The common multiples of 39 and 14 are n x 546, intersecting the two sets above,
- In the intersection multiples of 39 ∩ multiples of 14 the least positive element is 546.
- Therefore, the least common multiple of 39 and 14 is 546.
Taking the above into account you also know how to find all the common multiples of 39 and 14, not just the smallest. In the next section we show you how to calculate the lcm of thirty-nine and fourteen by means of two more methods.
How to find the LCM of 39 and 14
The least common multiple of 39 and 14 can be computed by using the greatest common factor aka gcf of 39 and 14. This is the easiest approach:
Alternatively, the lcm of 39 and 14 can be found using the prime factorization of 39 and 14:
- The prime factorization of 39 is: 3 x 13
- The prime factorization of 14 is: 2 x 7
- Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(39,39) = 546
In any case, the easiest way to compute the lcm of two numbers like 39 and 14 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 39,14. Push the button only to start over.
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Use of LCM of 39 and 14
What is the least common multiple of 39 and 14 used for? Answer: It is helpful for adding and subtracting fractions like 1/39 and 1/14. Just multiply the dividends and divisors by 14 and 39, respectively, such that the divisors have the value of 546, the lcm of 39 and 14.
Properties of LCM of 39 and 14
The most important properties of the lcm(39,14) are:
- Commutative property: lcm(39,14) = lcm(14,39)
- Associative property: lcm(39,14,n) = lcm(lcm(14,39),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 39 and 14 is 546. In common notation: lcm (39,14) = 546.
If you have been searching for lcm 39 and 14 or lcm 39 14 then you have come to the correct page, too. The same is the true if you typed lcm for 39 and 14 in your favorite search engine.
Note that you can find the least common multiple of many integer pairs including thirty-nine / fourteen by using the search form in the sidebar of this page.
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