LCM of 21 and 53


The lcm of 21 and 53 is the smallest positive integer that divides the numbers 21 and 53 without a remainder. Spelled out, it is the least common multiple of 21 and 53. Here you can find the lcm of 21 and 53, 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 21 and 53, but also that of three or more integers including twenty-one and fifty-three for example. Keep reading to learn everything about the lcm (21,53) and the terms related to it.

What is the LCM of 21 and 53

If you just want to know what is the least common multiple of 21 and 53, it is 1113. Usually, this is written as

lcm(21,53) = 1113

The lcm of 21 and 53 can be obtained like this:

  • The multiples of 21 are … , 1092, 1113, 1134, ….
  • The multiples of 53 are …, 1060, 1113, 1166, …
  • The common multiples of 21 and 53 are n x 1113, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 21 ∩ multiples of 53 the least positive element is 1113.
  • Therefore, the least common multiple of 21 and 53 is 1113.

Taking the above into account you also know how to find all the common multiples of 21 and 53, not just the smallest. In the next section we show you how to calculate the lcm of twenty-one and fifty-three by means of two more methods.

How to find the LCM of 21 and 53

The least common multiple of 21 and 53 can be computed by using the greatest common factor aka gcf of 21 and 53. This is the easiest approach:

lcm (21,53) = $\frac{21 \times 53}{gcf(21,53)} = \frac{1113}{1}$ = 1113

Alternatively, the lcm of 21 and 53 can be found using the prime factorization of 21 and 53:

  • The prime factorization of 21 is: 3 x 7
  • The prime factorization of 53 is: 53
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(21,21) = 1113

In any case, the easiest way to compute the lcm of two numbers like 21 and 53 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 21,53. Push the button only to start over.

The lcm is...
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Use of LCM of 21 and 53

What is the least common multiple of 21 and 53 used for? Answer: It is helpful for adding and subtracting fractions like 1/21 and 1/53. Just multiply the dividends and divisors by 53 and 21, respectively, such that the divisors have the value of 1113, the lcm of 21 and 53.

$\frac{1}{21} + \frac{1}{53} = \frac{53}{1113} + \frac{21}{1113} = \frac{74}{1113}$. $\hspace{30px}\frac{1}{21} – \frac{1}{53} = \frac{53}{1113} – \frac{21}{1113} = \frac{32}{1113}$.

Properties of LCM of 21 and 53

The most important properties of the lcm(21,53) are:

  • Commutative property: lcm(21,53) = lcm(53,21)
  • Associative property: lcm(21,53,n) = lcm(lcm(53,21),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 21 and 53 is 1113. In common notation: lcm (21,53) = 1113.

If you have been searching for lcm 21 and 53 or lcm 21 53 then you have come to the correct page, too. The same is the true if you typed lcm for 21 and 53 in your favorite search engine.

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

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