LCM of 6 and 95


The lcm of 6 and 95 is the smallest positive integer that divides the numbers 6 and 95 without a remainder. Spelled out, it is the least common multiple of 6 and 95. Here you can find the lcm of 6 and 95, 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 95, but also that of three or more integers including six and ninety-five for example. Keep reading to learn everything about the lcm (6,95) and the terms related to it.

What is the LCM of 6 and 95

If you just want to know what is the least common multiple of 6 and 95, it is 570. Usually, this is written as

lcm(6,95) = 570

The lcm of 6 and 95 can be obtained like this:

  • The multiples of 6 are …, 564, 570, 576, ….
  • The multiples of 95 are …, 475, 570, 665, …
  • The common multiples of 6 and 95 are n x 570, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 6 ∩ multiples of 95 the least positive element is 570.
  • Therefore, the least common multiple of 6 and 95 is 570.

Taking the above into account you also know how to find all the common multiples of 6 and 95, not just the smallest. In the next section we show you how to calculate the lcm of six and ninety-five by means of two more methods.

How to find the LCM of 6 and 95

The least common multiple of 6 and 95 can be computed by using the greatest common factor aka gcf of 6 and 95. This is the easiest approach:

lcm (6,95) = $\frac{6 \times 95}{gcf(6,95)} = \frac{570}{1}$ = 570

Alternatively, the lcm of 6 and 95 can be found using the prime factorization of 6 and 95:

  • The prime factorization of 6 is: 2 x 3
  • The prime factorization of 95 is: 5 x 19
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(6,6) = 570

In any case, the easiest way to compute the lcm of two numbers like 6 and 95 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 6,95. Push the button only to start over.

The lcm is...
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Use of LCM of 6 and 95

What is the least common multiple of 6 and 95 used for? Answer: It is helpful for adding and subtracting fractions like 1/6 and 1/95. Just multiply the dividends and divisors by 95 and 6, respectively, such that the divisors have the value of 570, the lcm of 6 and 95.

$\frac{1}{6} + \frac{1}{95} = \frac{95}{570} + \frac{6}{570} = \frac{101}{570}$. $\hspace{30px}\frac{1}{6} – \frac{1}{95} = \frac{95}{570} – \frac{6}{570} = \frac{89}{570}$.

Properties of LCM of 6 and 95

The most important properties of the lcm(6,95) are:

  • Commutative property: lcm(6,95) = lcm(95,6)
  • Associative property: lcm(6,95,n) = lcm(lcm(95,6),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 95 is 570. In common notation: lcm (6,95) = 570.

If you have been searching for lcm 6 and 95 or lcm 6 95 then you have come to the correct page, too. The same is the true if you typed lcm for 6 and 95 in your favorite search engine.

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

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