Home » Least Common Multiple » LCM of 51 and 42

LCM of 51 and 42

The lcm of 51 and 42 is the smallest positive integer that divides the numbers 51 and 42 without a remainder. Spelled out, it is the least common multiple of 51 and 42. Here you can find the result for 51 and 42, along with a total of three methods for computing it.


714

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 51 and 42, but also that of three or more integers including fifty-one and forty-two for example. Keep reading to learn everything about the lcm (51,42) and the terms related to it.

What is the Least Common Multiple of 51 and 42?

If you just want to know what is the least common multiple of 51 and 42, it is 714. Usually, this is written as

lcm(51,42) = 714


The lcm of 51 and 42 can be obtained like this:
  • The multiples of 51 are … , 663, 714, 765, ….
  • The multiples of 42 are …, 672, 714, 756, …
  • The common multiples of 51 and 42 are n x 714, intersecting the two sets above, .
  • In the intersection multiples of 51 ∩ multiples of 42 the least positive element is 714.
  • Therefore, the least common multiple of 51 and 42 is 714.

Taking the above into account you also know how to find all the common multiples of 51 and 42, not just the smallest. In the next section we show you how to calculate the lcm of fifty-one and forty-two by means of two more methods.

How to find the LCM of 51 and 42

The least common multiple of 51 and 42 can be computed by using the greatest common factor aka gcf of 51 and 42. This is the easiest approach:

lcm (51,42) = = 714



Alternatively, the lcm of 51 and 42 can be found using the prime factorization of 51 and 42:
  • The prime factorization of 51 is: 3 x 17
  • The prime factorization of 42 is: 2 x 3 x 7
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(51,51) = 714

In any case, the easiest way to compute the result for two numbers like 51 and 42 is by using our calculator above. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 51,422,2. Push the button only to start over.

Similar searched terms on our site also include:

In the next paragraph we explain how the mathematical concept can be employed.

Keep reading – it’s really interesting.

Use of Least Common Multiple of 51 and 42

What is the least common multiple of 51 and 42 used for? Answer: It is helpful for adding and subtracting fractions like 1/51 and 1/42. Just multiply the dividends and divisors by 14 and 17, respectively, such that the divisors have the value of 714, the lcm of 51 and 42.

. .

Next, we shed a light on the mathematical properties.

Properties of LCM of 51 and 42

The most important properties of the lcm(51,42) are:

  • Commutative property: lcm(51,42) = lcm(42,51)
  • Associative property: lcm(51,42,n) = lcm(lcm(42,51),n)

The associativity is particularly useful to get the lcm of three or more numbers; our calculator makes use of it.

Summary

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

Questions and comments 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 51 and 42 has been useful to you, and make sure to bookmark our site.

If you have some time left check out the related sites and resources in the sidebar of this site.

Thanks for your visit.

– Article written by Mark, last updated on August 8th, 2023