The lcm of 10 and 72 is the smallest positive integer that divides the numbers 10 and 72 without a remainder. Spelled out, it is the least common multiple of 10 and 72. Here you can find the lcm of 10 and 72, along with a total of three methods for computing it.
What is the LCM of 10 and 72
If you just want to know what is the least common multiple of 10 and 72, it is 360. Usually, this is written as
The lcm of 10 and 72 can be obtained like this:
- The multiples of 10 are … , 350, 360, 370, ….
- The multiples of 72 are …, 288, 360, 432, …
- The common multiples of 10 and 72 are n x 360, intersecting the two sets above,
- In the intersection multiples of 10 ∩ multiples of 72 the least positive element is 360.
- Therefore, the least common multiple of 10 and 72 is 360.
Taking the above into account you also know how to find all the common multiples of 10 and 72, not just the smallest. In the next section we show you how to calculate the lcm of ten and seventy-two by means of two more methods.
How to find the LCM of 10 and 72
The least common multiple of 10 and 72 can be computed by using the greatest common factor aka gcf of 10 and 72. This is the easiest approach:
Alternatively, the lcm of 10 and 72 can be found using the prime factorization of 10 and 72:
- The prime factorization of 10 is: 2 x 5
- The prime factorization of 72 is: 2 x 2 x 2 x 3 x 3
- Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(10,10) = 360
In any case, the easiest way to compute the lcm of two numbers like 10 and 72 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 10,72. Push the button only to start over.
Similar searched terms on our site also include:
Use of LCM of 10 and 72
What is the least common multiple of 10 and 72 used for? Answer: It is helpful for adding and subtracting fractions like 1/10 and 1/72. Just multiply the dividends and divisors by 36 and 5, respectively, such that the divisors have the value of 360, the lcm of 10 and 72.
Properties of LCM of 10 and 72
The most important properties of the lcm(10,72) are:
- Commutative property: lcm(10,72) = lcm(72,10)
- Associative property: lcm(10,72,n) = lcm(lcm(72,10),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 10 and 72 is 360. In common notation: lcm (10,72) = 360.
If you have been searching for lcm 10 and 72 or lcm 10 72 then you have come to the correct page, too. The same is the true if you typed lcm for 10 and 72 in your favorite search engine.
Note that you can find the least common multiple of many integer pairs including ten / seventy-two by using the search form in the sidebar of this page.
Questions and comments related to the lcm of 10 and 72 are really appreciated. Use the form below or send us a mail to get in touch.
Please hit the sharing buttons if our article about the least common multiple of 10 and 72 has been useful to you, and make sure to bookmark our site.
Thanks for your visit.