LCM of 10 and 14


The lcm of 10 and 14 is the smallest positive integer that divides the numbers 10 and 14 without a remainder. Spelled out, it is the least common multiple of 10 and 14. Here you can find the lcm of 10 and 14, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the lcm of 10 and 14, but also that of three or more integers including ten and fourteen for example. Keep reading to learn everything about the lcm (10,14) and the terms related to it.

What is the LCM of 10 and 14

If you just want to know what is the least common multiple of 10 and 14, it is 70. Usually, this is written as

lcm(10,14) = 70

The lcm of 10 and 14 can be obtained like this:

  • The multiples of 10 are …, 60, 70, 80, ….
  • The multiples of 14 are …, 56, 70, 84, …
  • The common multiples of 10 and 14 are n x 70, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 10 ∩ multiples of 14 the least positive element is 70.
  • Therefore, the least common multiple of 10 and 14 is 70.

Taking the above into account you also know how to find all the common multiples of 10 and 14, not just the smallest. In the next section we show you how to calculate the lcm of ten and fourteen by means of two more methods.

How to find the LCM of 10 and 14

The least common multiple of 10 and 14 can be computed by using the greatest common factor aka gcf of 10 and 14. This is the easiest approach:

lcm (10,14) = $\frac{10 \times 14}{gcf(10,14)} = \frac{140}{2}$ = 70

Alternatively, the lcm of 10 and 14 can be found using the prime factorization of 10 and 14:

  • The prime factorization of 10 is: 2 x 5
  • 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(10,10) = 70

In any case, the easiest way to compute the lcm of two numbers like 10 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 10,14. Push the button only to start over.

The lcm is...
Frequently searched terms on our site also include:

Use of LCM of 10 and 14

What is the least common multiple of 10 and 14 used for? Answer: It is helpful for adding and subtracting fractions like 1/10 and 1/14. Just multiply the dividends and divisors by 7 and 5, respectively, such that the divisors have the value of 70, the lcm of 10 and 14.

$\frac{1}{10} + \frac{1}{14} = \frac{7}{70} + \frac{5}{70} = \frac{12}{70}$. $\hspace{30px}\frac{1}{10} – \frac{1}{14} = \frac{7}{70} – \frac{5}{70} = \frac{2}{70}$.

Properties of LCM of 10 and 14

The most important properties of the lcm(10,14) are:

  • Commutative property: lcm(10,14) = lcm(14,10)
  • Associative property: lcm(10,14,n) = lcm(lcm(14,10),n) $\hspace{10px}n\neq 0 \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$

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 10 and 14 is 70. In common notation: lcm (10,14) = 70.

If you have been searching for lcm 10 and 14 or lcm 10 14 then you have come to the correct page, too. The same is the true if you typed lcm for 10 and 14 in your favorite search engine.

Note that you can find the least common multiple of many integer pairs including ten / fourteen by using the search form in the sidebar of this page.

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