LCM of 6 and 10

The lcm of 6 and 10 is the smallest positive integer that divides the numbers 6 and 10 without a remainder. Spelled out, it is the least common multiple of 6 and 10. Here you can find the lcm of 6 and 10, 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 6 and 10, but also that of three or more integers including six and ten for example. Keep reading to learn everything about the lcm (6,10) and the terms related to it.

What is the LCM of 6 and 10

If you just want to know what is the least common multiple of 6 and 10, it is 30. Usually, this is written as

lcm(6,10) = 30

The lcm of 6 and 10 can be obtained like this:

  • The multiples of 6 are …, 24, 30, 36, ….
  • The multiples of 10 are …, 20, 30, 40, …
  • The common multiples of 6 and 10 are n x 30, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 6 ∩ multiples of 10 the least positive element is 30.
  • Therefore, the least common multiple of 6 and 10 is 30.

Taking the above into account you also know how to find all the common multiples of 6 and 10, not just the smallest. In the next section we show you how to calculate the lcm of six and ten by means of two more methods.

How to find the LCM of 6 and 10

The least common multiple of 6 and 10 can be computed by using the greatest common factor aka gcf of 6 and 10. This is the easiest approach:

lcm (6,10) = $\frac{6 \times 10}{gcf(6,10)} = \frac{60}{2}$ = 30

Alternatively, the lcm of 6 and 10 can be found using the prime factorization of 6 and 10:

  • The prime factorization of 6 is: 2 x 3
  • The prime factorization of 10 is: 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(6,6) = 30

In any case, the easiest way to compute the lcm of two numbers like 6 and 10 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 6,10. Push the button only to start over.

The lcm is...
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Use of LCM of 6 and 10

What is the least common multiple of 6 and 10 used for? Answer: It is helpful for adding and subtracting fractions like 1/6 and 1/10. Just multiply the dividends and divisors by 5 and 3, respectively, such that the divisors have the value of 30, the lcm of 6 and 10.

$\frac{1}{6} + \frac{1}{10} = \frac{5}{30} + \frac{3}{30} = \frac{8}{30}$. $\hspace{30px}\frac{1}{6} – \frac{1}{10} = \frac{5}{30} – \frac{3}{30} = \frac{2}{30}$.

Properties of LCM of 6 and 10

The most important properties of the lcm(6,10) are:

  • Commutative property: lcm(6,10) = lcm(10,6)
  • Associative property: lcm(6,10,n) = lcm(lcm(10,6),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 6 and 10 is 30. In common notation: lcm (6,10) = 30.

If you have been searching for lcm 6 and 10 or lcm 6 10 then you have come to the correct page, too. The same is the true if you typed lcm for 6 and 10 in your favorite search engine.

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

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