LCM of 12 and 15


The lcm of 12 and 15 is the smallest positive integer that divides the numbers 12 and 15 without a remainder. Spelled out, it is the least common multiple of 12 and 15. Here you can find the lcm of 12 and 15, 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 12 and 15, but also that of three or more integers including twelve and fifteen for example. Keep reading to learn everything about the lcm (12,15) and the terms related to it.

What is the LCM of 12 and 15

If you just want to know what is the least common multiple of 12 and 15, it is 60. Usually, this is written as

lcm(12,15) = 60

The lcm of 12 and 15 can be obtained like this:

  • The multiples of 12 are …, 48, 60, 72, ….
  • The multiples of 15 are …, 45, 60, 75, …
  • The common multiples of 12 and 15 are n x 60, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 12 ∩ multiples of 15 the least positive element is 60.
  • Therefore, the least common multiple of 12 and 15 is 60.

Taking the above into account you also know how to find all the common multiples of 12 and 15, not just the smallest. In the next section we show you how to calculate the lcm of twelve and fifteen by means of two more methods.

How to find the LCM of 12 and 15

The least common multiple of 12 and 15 can be computed by using the greatest common factor aka gcf of 12 and 15. This is the easiest approach:

lcm (12,15) = $\frac{12 \times 15}{gcf(12,15)} = \frac{180}{3}$ = 60

Alternatively, the lcm of 12 and 15 can be found using the prime factorization of 12 and 15:

  • The prime factorization of 12 is: 2 x 2 x 3
  • The prime factorization of 15 is: 3 x 5
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(12,12) = 60

In any case, the easiest way to compute the lcm of two numbers like 12 and 15 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 12,15. Push the button only to start over.

The lcm is...
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Use of LCM of 12 and 15

What is the least common multiple of 12 and 15 used for? Answer: It is helpful for adding and subtracting fractions like 1/12 and 1/15. Just multiply the dividends and divisors by 5 and 4, respectively, such that the divisors have the value of 60, the lcm of 12 and 15.

$\frac{1}{12} + \frac{1}{15} = \frac{5}{60} + \frac{4}{60} = \frac{9}{60}$. $\hspace{30px}\frac{1}{12} – \frac{1}{15} = \frac{5}{60} – \frac{4}{60} = \frac{1}{60}$.

Properties of LCM of 12 and 15

The most important properties of the lcm(12,15) are:

  • Commutative property: lcm(12,15) = lcm(15,12)
  • Associative property: lcm(12,15,n) = lcm(lcm(15,12),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 12 and 15 is 60. In common notation: lcm (12,15) = 60.

If you have been searching for lcm 12 and 15 or lcm 12 15 then you have come to the correct page, too. The same is the true if you typed lcm for 12 and 15 in your favorite search engine.

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

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