The lcm of 14 and 40 is the smallest positive integer that divides the numbers 14 and 40 without a remainder. Spelled out, it is the least common multiple of 14 and 40. Here you can find the lcm of 14 and 40, along with a total of three methods for computing it.
What is the LCM of 14 and 40
If you just want to know what is the least common multiple of 14 and 40, it is 280. Usually, this is written as
The lcm of 14 and 40 can be obtained like this:
- The multiples of 14 are … , 266, 280, 294, ….
- The multiples of 40 are …, 240, 280, 320, …
- The common multiples of 14 and 40 are n x 280, intersecting the two sets above,
- In the intersection multiples of 14 ∩ multiples of 40 the least positive element is 280.
- Therefore, the least common multiple of 14 and 40 is 280.
Taking the above into account you also know how to find all the common multiples of 14 and 40, not just the smallest. In the next section we show you how to calculate the lcm of fourteen and forty by means of two more methods.
How to find the LCM of 14 and 40
The least common multiple of 14 and 40 can be computed by using the greatest common factor aka gcf of 14 and 40. This is the easiest approach:
Alternatively, the lcm of 14 and 40 can be found using the prime factorization of 14 and 40:
- The prime factorization of 14 is: 2 x 7
- The prime factorization of 40 is: 2 x 2 x 2 x 5
- Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(14,14) = 280
In any case, the easiest way to compute the lcm of two numbers like 14 and 40 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 14,40. Push the button only to start over.
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Use of LCM of 14 and 40
What is the least common multiple of 14 and 40 used for? Answer: It is helpful for adding and subtracting fractions like 1/14 and 1/40. Just multiply the dividends and divisors by 20 and 7, respectively, such that the divisors have the value of 280, the lcm of 14 and 40.
Properties of LCM of 14 and 40
The most important properties of the lcm(14,40) are:
- Commutative property: lcm(14,40) = lcm(40,14)
- Associative property: lcm(14,40,n) = lcm(lcm(40,14),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 14 and 40 is 280. In common notation: lcm (14,40) = 280.
If you have been searching for lcm 14 and 40 or lcm 14 40 then you have come to the correct page, too. The same is the true if you typed lcm for 14 and 40 in your favorite search engine.
Note that you can find the least common multiple of many integer pairs including fourteen / forty by using the search form in the sidebar of this page.
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