LCM of 18 and 25

The lcm of 18 and 25 is the smallest positive integer that divides the numbers 18 and 25 without a remainder. Spelled out, it is the least common multiple of 18 and 25. Here you can find the lcm of 18 and 25, 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 18 and 25, but also that of three or more integers including eighteen and twenty-five for example. Keep reading to learn everything about the lcm (18,25) and the terms related to it.

What is the LCM of 18 and 25

If you just want to know what is the least common multiple of 18 and 25, it is 450. Usually, this is written as

lcm(18,25) = 450

The lcm of 18 and 25 can be obtained like this:

  • The multiples of 18 are …, 432, 450, 468, ….
  • The multiples of 25 are …, 425, 450, 475, …
  • The common multiples of 18 and 25 are n x 450, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 18 ∩ multiples of 25 the least positive element is 450.
  • Therefore, the least common multiple of 18 and 25 is 450.

Taking the above into account you also know how to find all the common multiples of 18 and 25, not just the smallest. In the next section we show you how to calculate the lcm of eighteen and twenty-five by means of two more methods.

How to find the LCM of 18 and 25

The least common multiple of 18 and 25 can be computed by using the greatest common factor aka gcf of 18 and 25. This is the easiest approach:

lcm (18,25) = $\frac{18 \times 25}{gcf(18,25)} = \frac{450}{1}$ = 450

Alternatively, the lcm of 18 and 25 can be found using the prime factorization of 18 and 25:

  • The prime factorization of 18 is: 2 x 3 x 3
  • The prime factorization of 25 is: 5 x 5
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(18,18) = 450

In any case, the easiest way to compute the lcm of two numbers like 18 and 25 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 18,25. Push the button only to start over.

The lcm is...
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Use of LCM of 18 and 25

What is the least common multiple of 18 and 25 used for? Answer: It is helpful for adding and subtracting fractions like 1/18 and 1/25. Just multiply the dividends and divisors by 25 and 18, respectively, such that the divisors have the value of 450, the lcm of 18 and 25.

$\frac{1}{18} + \frac{1}{25} = \frac{25}{450} + \frac{18}{450} = \frac{43}{450}$. $\hspace{30px}\frac{1}{18} – \frac{1}{25} = \frac{25}{450} – \frac{18}{450} = \frac{7}{450}$.

Properties of LCM of 18 and 25

The most important properties of the lcm(18,25) are:

  • Commutative property: lcm(18,25) = lcm(25,18)
  • Associative property: lcm(18,25,n) = lcm(lcm(25,18),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 18 and 25 is 450. In common notation: lcm (18,25) = 450.

If you have been searching for lcm 18 and 25 or lcm 18 25 then you have come to the correct page, too. The same is the true if you typed lcm for 18 and 25 in your favorite search engine.

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

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