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LCM of 21 and 47

The lcm of 21 and 47 is the smallest positive integer that divides the numbers 21 and 47 without a remainder. Spelled out, it is the least common multiple of 21 and 47. Here you can find the result for 21 and 47, along with a total of three methods for computing it.


987

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 21 and 47, but also that of three or more integers including twenty-one and forty-seven for example. Keep reading to learn everything about the lcm (21,47) and the terms related to it.

What is the Least Common Multiple of 21 and 47?

If you just want to know what is the least common multiple of 21 and 47, it is 987. Usually, this is written as

lcm(21,47) = 987


The lcm of 21 and 47 can be obtained like this:
  • The multiples of 21 are … , 966, 987, 1008, ….
  • The multiples of 47 are …, 940, 987, 1034, …
  • The common multiples of 21 and 47 are n x 987, intersecting the two sets above, .
  • In the intersection multiples of 21 ∩ multiples of 47 the least positive element is 987.
  • Therefore, the least common multiple of 21 and 47 is 987.

Taking the above into account you also know how to find all the common multiples of 21 and 47, not just the smallest. In the next section we show you how to calculate the lcm of twenty-one and forty-seven by means of two more methods.

How to find the LCM of 21 and 47

The least common multiple of 21 and 47 can be computed by using the greatest common factor aka gcf of 21 and 47. This is the easiest approach:

lcm (21,47) = = 987



Alternatively, the lcm of 21 and 47 can be found using the prime factorization of 21 and 47:
  • The prime factorization of 21 is: 3 x 7
  • The prime factorization of 47 is: 47
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(21,21) = 987

In any case, the easiest way to compute the result for two numbers like 21 and 47 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 21,472,2. 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 21 and 47

What is the least common multiple of 21 and 47 used for? Answer: It is helpful for adding and subtracting fractions like 1/21 and 1/47. Just multiply the dividends and divisors by 47 and 21, respectively, such that the divisors have the value of 987, the lcm of 21 and 47.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 21 and 47

The most important properties of the lcm(21,47) are:

  • Commutative property: lcm(21,47) = lcm(47,21)
  • Associative property: lcm(21,47,n) = lcm(lcm(47,21),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 twenty-one / forty-seven by using the the search form in the sidebar of this page.

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