LCM of 25 and 49


The lcm of 25 and 49 is the smallest positive integer that divides the numbers 25 and 49 without a remainder. Spelled out, it is the least common multiple of 25 and 49. Here you can find the lcm of 25 and 49, 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 49, but also that of three or more integers including twenty-five and forty-nine for example. Keep reading to learn everything about the lcm (25,49) and the terms related to it.

What is the LCM of 25 and 49

If you just want to know what is the least common multiple of 25 and 49, it is 1225. Usually, this is written as

lcm(25,49) = 1225

The lcm of 25 and 49 can be obtained like this:

  • The multiples of 25 are …, 1200, 1225, 1250, ….
  • The multiples of 49 are …, 1176, 1225, 1274, …
  • The common multiples of 25 and 49 are n x 1225, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 25 ∩ multiples of 49 the least positive element is 1225.
  • Therefore, the least common multiple of 25 and 49 is 1225.

Taking the above into account you also know how to find all the common multiples of 25 and 49, not just the smallest. In the next section we show you how to calculate the lcm of twenty-five and forty-nine by means of two more methods.

How to find the LCM of 25 and 49

The least common multiple of 25 and 49 can be computed by using the greatest common factor aka gcf of 25 and 49. This is the easiest approach:

lcm (25,49) = $\frac{25 \times 49}{gcf(25,49)} = \frac{1225}{1}$ = 1225

Alternatively, the lcm of 25 and 49 can be found using the prime factorization of 25 and 49:

  • The prime factorization of 25 is: 5 x 5
  • The prime factorization of 49 is: 7 x 7
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(25,25) = 1225

In any case, the easiest way to compute the lcm of two numbers like 25 and 49 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 25,49. Push the button only to start over.

The lcm is...
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Use of LCM of 25 and 49

What is the least common multiple of 25 and 49 used for? Answer: It is helpful for adding and subtracting fractions like 1/25 and 1/49. Just multiply the dividends and divisors by 49 and 25, respectively, such that the divisors have the value of 1225, the lcm of 25 and 49.

$\frac{1}{25} + \frac{1}{49} = \frac{49}{1225} + \frac{25}{1225} = \frac{74}{1225}$. $\hspace{30px}\frac{1}{25} – \frac{1}{49} = \frac{49}{1225} – \frac{25}{1225} = \frac{24}{1225}$.

Properties of LCM of 25 and 49

The most important properties of the lcm(25,49) are:

  • Commutative property: lcm(25,49) = lcm(49,25)
  • Associative property: lcm(25,49,n) = lcm(lcm(49,25),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 49 is 1225. In common notation: lcm (25,49) = 1225.

If you have been searching for lcm 25 and 49 or lcm 25 49 then you have come to the correct page, too. The same is the true if you typed lcm for 25 and 49 in your favorite search engine.

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

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