LCM of 11 and 64


The lcm of 11 and 64 is the smallest positive integer that divides the numbers 11 and 64 without a remainder. Spelled out, it is the least common multiple of 11 and 64. Here you can find the lcm of 11 and 64, 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 11 and 64, but also that of three or more integers including eleven and sixty-four for example. Keep reading to learn everything about the lcm (11,64) and the terms related to it.

What is the LCM of 11 and 64

If you just want to know what is the least common multiple of 11 and 64, it is 704. Usually, this is written as

lcm(11,64) = 704

The lcm of 11 and 64 can be obtained like this:

  • The multiples of 11 are …, 693, 704, 715, ….
  • The multiples of 64 are …, 640, 704, 768, …
  • The common multiples of 11 and 64 are n x 704, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 11 ∩ multiples of 64 the least positive element is 704.
  • Therefore, the least common multiple of 11 and 64 is 704.

Taking the above into account you also know how to find all the common multiples of 11 and 64, not just the smallest. In the next section we show you how to calculate the lcm of eleven and sixty-four by means of two more methods.

How to find the LCM of 11 and 64

The least common multiple of 11 and 64 can be computed by using the greatest common factor aka gcf of 11 and 64. This is the easiest approach:

lcm (11,64) = $\frac{11 \times 64}{gcf(11,64)} = \frac{704}{1}$ = 704

Alternatively, the lcm of 11 and 64 can be found using the prime factorization of 11 and 64:

  • The prime factorization of 11 is: 11
  • The prime factorization of 64 is: 2 x 2 x 2 x 2 x 2 x 2
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(11,11) = 704

In any case, the easiest way to compute the lcm of two numbers like 11 and 64 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 11,64. Push the button only to start over.

The lcm is...
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Use of LCM of 11 and 64

What is the least common multiple of 11 and 64 used for? Answer: It is helpful for adding and subtracting fractions like 1/11 and 1/64. Just multiply the dividends and divisors by 64 and 11, respectively, such that the divisors have the value of 704, the lcm of 11 and 64.

$\frac{1}{11} + \frac{1}{64} = \frac{64}{704} + \frac{11}{704} = \frac{75}{704}$. $\hspace{30px}\frac{1}{11} – \frac{1}{64} = \frac{64}{704} – \frac{11}{704} = \frac{53}{704}$.

Properties of LCM of 11 and 64

The most important properties of the lcm(11,64) are:

  • Commutative property: lcm(11,64) = lcm(64,11)
  • Associative property: lcm(11,64,n) = lcm(lcm(64,11),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 11 and 64 is 704. In common notation: lcm (11,64) = 704.

If you have been searching for lcm 11 and 64 or lcm 11 64 then you have come to the correct page, too. The same is the true if you typed lcm for 11 and 64 in your favorite search engine.

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

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