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LCM of 28 and 68

The lcm of 28 and 68 is the smallest positive integer that divides the numbers 28 and 68 without a remainder. Spelled out, it is the least common multiple of 28 and 68. Here you can find the result for 28 and 68, along with a total of three methods for computing it.


476

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 28 and 68, but also that of three or more integers including twenty-eight and sixty-eight for example. Keep reading to learn everything about the lcm (28,68) and the terms related to it.

What is the Least Common Multiple of 28 and 68?

If you just want to know what is the least common multiple of 28 and 68, it is 476. Usually, this is written as

lcm(28,68) = 476


The lcm of 28 and 68 can be obtained like this:
  • The multiples of 28 are … , 448, 476, 504, ….
  • The multiples of 68 are …, 408, 476, 544, …
  • The common multiples of 28 and 68 are n x 476, intersecting the two sets above, .
  • In the intersection multiples of 28 ∩ multiples of 68 the least positive element is 476.
  • Therefore, the least common multiple of 28 and 68 is 476.

Taking the above into account you also know how to find all the common multiples of 28 and 68, not just the smallest. In the next section we show you how to calculate the lcm of twenty-eight and sixty-eight by means of two more methods.

How to find the LCM of 28 and 68

The least common multiple of 28 and 68 can be computed by using the greatest common factor aka gcf of 28 and 68. This is the easiest approach:

lcm (28,68) = = 476



Alternatively, the lcm of 28 and 68 can be found using the prime factorization of 28 and 68:
  • The prime factorization of 28 is: 2 x 2 x 7
  • The prime factorization of 68 is: 2 x 2 x 17
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(28,28) = 476

In any case, the easiest way to compute the result for two numbers like 28 and 68 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 28,682,2. 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 28 and 68

What is the least common multiple of 28 and 68 used for? Answer: It is helpful for adding and subtracting fractions like 1/28 and 1/68. Just multiply the dividends and divisors by 17 and 7, respectively, such that the divisors have the value of 476, the lcm of 28 and 68.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 28 and 68

The most important properties of the lcm(28,68) are:

  • Commutative property: lcm(28,68) = lcm(68,28)
  • Associative property: lcm(28,68,n) = lcm(lcm(68,28),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-eight / sixty-eight 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