LCM of 25 and 76


The lcm of 25 and 76 is the smallest positive integer that divides the numbers 25 and 76 without a remainder. Spelled out, it is the least common multiple of 25 and 76. Here you can find the lcm of 25 and 76, 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 25 and 76, but also that of three or more integers including twenty-five and seventy-six for example. Keep reading to learn everything about the lcm (25,76) and the terms related to it.

What is the LCM of 25 and 76

If you just want to know what is the least common multiple of 25 and 76, it is 1900. Usually, this is written as

lcm(25,76) = 1900

The lcm of 25 and 76 can be obtained like this:

  • The multiples of 25 are …, 1875, 1900, 1925, ….
  • The multiples of 76 are …, 1824, 1900, 1976, …
  • The common multiples of 25 and 76 are n x 1900, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 25 ∩ multiples of 76 the least positive element is 1900.
  • Therefore, the least common multiple of 25 and 76 is 1900.

Taking the above into account you also know how to find all the common multiples of 25 and 76, not just the smallest. In the next section we show you how to calculate the lcm of twenty-five and seventy-six by means of two more methods.

How to find the LCM of 25 and 76

The least common multiple of 25 and 76 can be computed by using the greatest common factor aka gcf of 25 and 76. This is the easiest approach:

lcm (25,76) = $\frac{25 \times 76}{gcf(25,76)} = \frac{1900}{1}$ = 1900

Alternatively, the lcm of 25 and 76 can be found using the prime factorization of 25 and 76:

  • The prime factorization of 25 is: 5 x 5
  • The prime factorization of 76 is: 2 x 2 x 19
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(25,25) = 1900

In any case, the easiest way to compute the lcm of two numbers like 25 and 76 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 25,76. Push the button only to start over.

The lcm is...
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Use of LCM of 25 and 76

What is the least common multiple of 25 and 76 used for? Answer: It is helpful for adding and subtracting fractions like 1/25 and 1/76. Just multiply the dividends and divisors by 76 and 25, respectively, such that the divisors have the value of 1900, the lcm of 25 and 76.

$\frac{1}{25} + \frac{1}{76} = \frac{76}{1900} + \frac{25}{1900} = \frac{101}{1900}$. $\hspace{30px}\frac{1}{25} – \frac{1}{76} = \frac{76}{1900} – \frac{25}{1900} = \frac{51}{1900}$.

Properties of LCM of 25 and 76

The most important properties of the lcm(25,76) are:

  • Commutative property: lcm(25,76) = lcm(76,25)
  • Associative property: lcm(25,76,n) = lcm(lcm(76,25),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 25 and 76 is 1900. In common notation: lcm (25,76) = 1900.

If you have been searching for lcm 25 and 76 or lcm 25 76 then you have come to the correct page, too. The same is the true if you typed lcm for 25 and 76 in your favorite search engine.

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

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