The lcm of 36 and 64 is the smallest positive integer that divides the numbers 36 and 64 without a remainder. Spelled out, it is the least common multiple of 36 and 64. Here you can find the lcm of 36 and 64, along with a total of three methods for computing it.
What is the LCM of 36 and 64
If you just want to know what is the least common multiple of 36 and 64, it is 576. Usually, this is written as
The lcm of 36 and 64 can be obtained like this:
- The multiples of 36 are … , 540, 576, 612, ….
- The multiples of 64 are …, 512, 576, 640, …
- The common multiples of 36 and 64 are n x 576, intersecting the two sets above,
- In the intersection multiples of 36 ∩ multiples of 64 the least positive element is 576.
- Therefore, the least common multiple of 36 and 64 is 576.
Taking the above into account you also know how to find all the common multiples of 36 and 64, not just the smallest. In the next section we show you how to calculate the lcm of thirty-six and sixty-four by means of two more methods.
How to find the LCM of 36 and 64
The least common multiple of 36 and 64 can be computed by using the greatest common factor aka gcf of 36 and 64. This is the easiest approach:
Alternatively, the lcm of 36 and 64 can be found using the prime factorization of 36 and 64:
- The prime factorization of 36 is: 2 x 2 x 3 x 3
- 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(36,36) = 576
In any case, the easiest way to compute the lcm of two numbers like 36 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 36,64. Push the button only to start over.
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Use of LCM of 36 and 64
What is the least common multiple of 36 and 64 used for? Answer: It is helpful for adding and subtracting fractions like 1/36 and 1/64. Just multiply the dividends and divisors by 16 and 9, respectively, such that the divisors have the value of 576, the lcm of 36 and 64.
Properties of LCM of 36 and 64
The most important properties of the lcm(36,64) are:
- Commutative property: lcm(36,64) = lcm(64,36)
- Associative property: lcm(36,64,n) = lcm(lcm(64,36),n)
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 36 and 64 is 576. In common notation: lcm (36,64) = 576.
If you have been searching for lcm 36 and 64 or lcm 36 64 then you have come to the correct page, too. The same is the true if you typed lcm for 36 and 64 in your favorite search engine.
Note that you can find the least common multiple of many integer pairs including thirty-six / sixty-four by using the search form in the sidebar of this page.
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