LCM of 15 and 40


The lcm of 15 and 40 is the smallest positive integer that divides the numbers 15 and 40 without a remainder. Spelled out, it is the least common multiple of 15 and 40. Here you can find the lcm of 15 and 40, 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 15 and 40, but also that of three or more integers including fifteen and forty for example. Keep reading to learn everything about the lcm (15,40) and the terms related to it.

What is the LCM of 15 and 40

If you just want to know what is the least common multiple of 15 and 40, it is 120. Usually, this is written as

lcm(15,40) = 120

The lcm of 15 and 40 can be obtained like this:

  • The multiples of 15 are …, 105, 120, 135, ….
  • The multiples of 40 are …, 80, 120, 160, …
  • The common multiples of 15 and 40 are n x 120, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 15 ∩ multiples of 40 the least positive element is 120.
  • Therefore, the least common multiple of 15 and 40 is 120.

Taking the above into account you also know how to find all the common multiples of 15 and 40, not just the smallest. In the next section we show you how to calculate the lcm of fifteen and forty by means of two more methods.

How to find the LCM of 15 and 40

The least common multiple of 15 and 40 can be computed by using the greatest common factor aka gcf of 15 and 40. This is the easiest approach:

lcm (15,40) = $\frac{15 \times 40}{gcf(15,40)} = \frac{600}{5}$ = 120

Alternatively, the lcm of 15 and 40 can be found using the prime factorization of 15 and 40:

  • The prime factorization of 15 is: 3 x 5
  • The prime factorization of 40 is: 2 x 2 x 2 x 5
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(15,15) = 120

In any case, the easiest way to compute the lcm of two numbers like 15 and 40 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 15,40. Push the button only to start over.

The lcm is...
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Use of LCM of 15 and 40

What is the least common multiple of 15 and 40 used for? Answer: It is helpful for adding and subtracting fractions like 1/15 and 1/40. Just multiply the dividends and divisors by 8 and 3, respectively, such that the divisors have the value of 120, the lcm of 15 and 40.

$\frac{1}{15} + \frac{1}{40} = \frac{8}{120} + \frac{3}{120} = \frac{11}{120}$. $\hspace{30px}\frac{1}{15} – \frac{1}{40} = \frac{8}{120} – \frac{3}{120} = \frac{5}{120}$.

Properties of LCM of 15 and 40

The most important properties of the lcm(15,40) are:

  • Commutative property: lcm(15,40) = lcm(40,15)
  • Associative property: lcm(15,40,n) = lcm(lcm(40,15),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 15 and 40 is 120. In common notation: lcm (15,40) = 120.

If you have been searching for lcm 15 and 40 or lcm 15 40 then you have come to the correct page, too. The same is the true if you typed lcm for 15 and 40 in your favorite search engine.

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

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