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LCM of 21 and 62

The lcm of 21 and 62 is the smallest positive integer that divides the numbers 21 and 62 without a remainder. Spelled out, it is the least common multiple of 21 and 62. Here you can find the result for 21 and 62, along with a total of three methods for computing it.


1302

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 62, but also that of three or more integers including twenty-one and sixty-two for example. Keep reading to learn everything about the lcm (21,62) and the terms related to it.

What is the Least Common Multiple of 21 and 62?

If you just want to know what is the least common multiple of 21 and 62, it is 1302. Usually, this is written as

lcm(21,62) = 1302


The lcm of 21 and 62 can be obtained like this:
  • The multiples of 21 are … , 1281, 1302, 1323, ….
  • The multiples of 62 are …, 1240, 1302, 1364, …
  • The common multiples of 21 and 62 are n x 1302, intersecting the two sets above, .
  • In the intersection multiples of 21 ∩ multiples of 62 the least positive element is 1302.
  • Therefore, the least common multiple of 21 and 62 is 1302.

Taking the above into account you also know how to find all the common multiples of 21 and 62, not just the smallest. In the next section we show you how to calculate the lcm of twenty-one and sixty-two by means of two more methods.

How to find the LCM of 21 and 62

The least common multiple of 21 and 62 can be computed by using the greatest common factor aka gcf of 21 and 62. This is the easiest approach:

lcm (21,62) = = 1302



Alternatively, the lcm of 21 and 62 can be found using the prime factorization of 21 and 62:
  • The prime factorization of 21 is: 3 x 7
  • The prime factorization of 62 is: 2 x 31
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(21,21) = 1302

In any case, the easiest way to compute the result for two numbers like 21 and 62 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 21,622,2. 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 62

What is the least common multiple of 21 and 62 used for? Answer: It is helpful for adding and subtracting fractions like 1/21 and 1/62. Just multiply the dividends and divisors by 62 and 21, respectively, such that the divisors have the value of 1302, the lcm of 21 and 62.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 21 and 62

The most important properties of the lcm(21,62) are:

  • Commutative property: lcm(21,62) = lcm(62,21)
  • Associative property: lcm(21,62,n) = lcm(lcm(62,21),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 / sixty-two 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