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LCM of 34 and 7

The lcm of 34 and 7 is the smallest positive integer that divides the numbers 34 and 7 without a remainder. Spelled out, it is the least common multiple of 34 and 7. Here you can find the result for 34 and 7, along with a total of three methods for computing it.


238

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 34 and 7, but also that of three or more integers including thirty-four and seven for example. Keep reading to learn everything about the lcm (34,7) and the terms related to it.

What is the Least Common Multiple of 34 and 7?

If you just want to know what is the least common multiple of 34 and 7, it is 238. Usually, this is written as

lcm(34,7) = 238


The lcm of 34 and 7 can be obtained like this:
  • The multiples of 34 are … , 204, 238, 272, ….
  • The multiples of 7 are …, 231, 238, 245, …
  • The common multiples of 34 and 7 are n x 238, intersecting the two sets above, .
  • In the intersection multiples of 34 ∩ multiples of 7 the least positive element is 238.
  • Therefore, the least common multiple of 34 and 7 is 238.

Taking the above into account you also know how to find all the common multiples of 34 and 7, not just the smallest. In the next section we show you how to calculate the lcm of thirty-four and seven by means of two more methods.

How to find the LCM of 34 and 7

The least common multiple of 34 and 7 can be computed by using the greatest common factor aka gcf of 34 and 7. This is the easiest approach:

lcm (34,7) = = 238



Alternatively, the lcm of 34 and 7 can be found using the prime factorization of 34 and 7:
  • The prime factorization of 34 is: 2 x 17
  • The prime factorization of 7 is: 7
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(34,34) = 238

In any case, the easiest way to compute the result for two numbers like 34 and 7 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 34,72,2. 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 34 and 7

What is the least common multiple of 34 and 7 used for? Answer: It is helpful for adding and subtracting fractions like 1/34 and 1/7. Just multiply the dividends and divisors by 7 and 34, respectively, such that the divisors have the value of 238, the lcm of 34 and 7.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 34 and 7

The most important properties of the lcm(34,7) are:

  • Commutative property: lcm(34,7) = lcm(7,34)
  • Associative property: lcm(34,7,n) = lcm(lcm(7,34),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 thirty-four / seven 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