LCM of 10 and 5


The lcm of 10 and 5 is the smallest positive integer that divides the numbers 10 and 5 without a remainder. Spelled out, it is the least common multiple of 10 and 5. Here you can find the lcm of 10 and 5, 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 5, but also that of three or more integers including ten and five for example. Keep reading to learn everything about the lcm (10,5) and the terms related to it.

What is the LCM of 10 and 5

If you just want to know what is the least common multiple of 10 and 5, it is 10. Usually, this is written as

lcm(10,5) = 10

The lcm of 10 and 5 can be obtained like this:

  • The multiples of 10 are …, 0, 10, 20, ….
  • The multiples of 5 are …, 5, 10, 15, …
  • The common multiples of 10 and 5 are n x 10, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 10 ∩ multiples of 5 the least positive element is 10.
  • Therefore, the least common multiple of 10 and 5 is 10.

Taking the above into account you also know how to find all the common multiples of 10 and 5, not just the smallest. In the next section we show you how to calculate the lcm of ten and five by means of two more methods.

How to find the LCM of 10 and 5

The least common multiple of 10 and 5 can be computed by using the greatest common factor aka gcf of 10 and 5. This is the easiest approach:

lcm (10,5) = $\frac{10 \times 5}{gcf(10,5)} = \frac{50}{5}$ = 10

Alternatively, the lcm of 10 and 5 can be found using the prime factorization of 10 and 5:

  • The prime factorization of 10 is: 2 x 5
  • The prime factorization of 5 is: 5
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(10,10) = 10

In any case, the easiest way to compute the lcm of two numbers like 10 and 5 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 10,5. Push the button only to start over.

The lcm is...
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Use of LCM of 10 and 5

What is the least common multiple of 10 and 5 used for? Answer: It is helpful for adding and subtracting fractions like 1/10 and 1/5. Just multiply the dividends and divisors by 1 and 2, respectively, such that the divisors have the value of 10, the lcm of 10 and 5.

$\frac{1}{10} + \frac{1}{5} = \frac{1}{10} + \frac{2}{10} = \frac{3}{10}$. $\hspace{30px}\frac{1}{10} – \frac{1}{5} = \frac{1}{10} – \frac{2}{10} = \frac{-1}{10}$.

Properties of LCM of 10 and 5

The most important properties of the lcm(10,5) are:

  • Commutative property: lcm(10,5) = lcm(5,10)
  • Associative property: lcm(10,5,n) = lcm(lcm(5,10),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 5 is 10. In common notation: lcm (10,5) = 10.

If you have been searching for lcm 10 and 5 or lcm 10 5 then you have come to the correct page, too. The same is the true if you typed lcm for 10 and 5 in your favorite search engine.

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

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