LCM of 42 and 54


The lcm of 42 and 54 is the smallest positive integer that divides the numbers 42 and 54 without a remainder. Spelled out, it is the least common multiple of 42 and 54. Here you can find the lcm of 42 and 54, 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 42 and 54, but also that of three or more integers including forty-two and fifty-four for example. Keep reading to learn everything about the lcm (42,54) and the terms related to it.

What is the LCM of 42 and 54

If you just want to know what is the least common multiple of 42 and 54, it is 378. Usually, this is written as

lcm(42,54) = 378

The lcm of 42 and 54 can be obtained like this:

  • The multiples of 42 are …, 336, 378, 420, ….
  • The multiples of 54 are …, 324, 378, 432, …
  • The common multiples of 42 and 54 are n x 378, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 42 ∩ multiples of 54 the least positive element is 378.
  • Therefore, the least common multiple of 42 and 54 is 378.

Taking the above into account you also know how to find all the common multiples of 42 and 54, not just the smallest. In the next section we show you how to calculate the lcm of forty-two and fifty-four by means of two more methods.

How to find the LCM of 42 and 54

The least common multiple of 42 and 54 can be computed by using the greatest common factor aka gcf of 42 and 54. This is the easiest approach:

lcm (42,54) = $\frac{42 \times 54}{gcf(42,54)} = \frac{2268}{6}$ = 378

Alternatively, the lcm of 42 and 54 can be found using the prime factorization of 42 and 54:

  • The prime factorization of 42 is: 2 x 3 x 7
  • The prime factorization of 54 is: 2 x 3 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(42,42) = 378

In any case, the easiest way to compute the lcm of two numbers like 42 and 54 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 42,54. Push the button only to start over.

The lcm is...
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Use of LCM of 42 and 54

What is the least common multiple of 42 and 54 used for? Answer: It is helpful for adding and subtracting fractions like 1/42 and 1/54. Just multiply the dividends and divisors by 9 and 7, respectively, such that the divisors have the value of 378, the lcm of 42 and 54.

$\frac{1}{42} + \frac{1}{54} = \frac{9}{378} + \frac{7}{378} = \frac{16}{378}$. $\hspace{30px}\frac{1}{42} – \frac{1}{54} = \frac{9}{378} – \frac{7}{378} = \frac{2}{378}$.

Properties of LCM of 42 and 54

The most important properties of the lcm(42,54) are:

  • Commutative property: lcm(42,54) = lcm(54,42)
  • Associative property: lcm(42,54,n) = lcm(lcm(54,42),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 42 and 54 is 378. In common notation: lcm (42,54) = 378.

If you have been searching for lcm 42 and 54 or lcm 42 54 then you have come to the correct page, too. The same is the true if you typed lcm for 42 and 54 in your favorite search engine.

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

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