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LCM of 14 and 63

The lcm of 14 and 63 is the smallest positive integer that divides the numbers 14 and 63 without a remainder. Spelled out, it is the least common multiple of 14 and 63. Here you can find the result for 14 and 63, along with a total of three methods for computing it.


126

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 14 and 63, but also that of three or more integers including fourteen and sixty-three for example. Keep reading to learn everything about the lcm (14,63) and the terms related to it.

What is the Least Common Multiple of 14 and 63?

If you just want to know what is the least common multiple of 14 and 63, it is 126. Usually, this is written as

lcm(14,63) = 126


The lcm of 14 and 63 can be obtained like this:
  • The multiples of 14 are … , 112, 126, 140, ….
  • The multiples of 63 are …, 63, 126, 189, …
  • The common multiples of 14 and 63 are n x 126, intersecting the two sets above, .
  • In the intersection multiples of 14 ∩ multiples of 63 the least positive element is 126.
  • Therefore, the least common multiple of 14 and 63 is 126.

Taking the above into account you also know how to find all the common multiples of 14 and 63, not just the smallest. In the next section we show you how to calculate the lcm of fourteen and sixty-three by means of two more methods.

How to find the LCM of 14 and 63

The least common multiple of 14 and 63 can be computed by using the greatest common factor aka gcf of 14 and 63. This is the easiest approach:

lcm (14,63) = = 126



Alternatively, the lcm of 14 and 63 can be found using the prime factorization of 14 and 63:
  • The prime factorization of 14 is: 2 x 7
  • The prime factorization of 63 is: 3 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(14,14) = 126

In any case, the easiest way to compute the result for two numbers like 14 and 63 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 14,632,2. 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 14 and 63

What is the least common multiple of 14 and 63 used for? Answer: It is helpful for adding and subtracting fractions like 1/14 and 1/63. Just multiply the dividends and divisors by 9 and 2, respectively, such that the divisors have the value of 126, the lcm of 14 and 63.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 14 and 63

The most important properties of the lcm(14,63) are:

  • Commutative property: lcm(14,63) = lcm(63,14)
  • Associative property: lcm(14,63,n) = lcm(lcm(63,14),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 fourteen / sixty-three by using the search form in the sidebar of this page.

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