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LCM of 33 and 34

The lcm of 33 and 34 is the smallest positive integer that divides the numbers 33 and 34 without a remainder. Spelled out, it is the least common multiple of 33 and 34. Here you can find the result for 33 and 34, along with a total of three methods for computing it.


1122

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 33 and 34, but also that of three or more integers including thirty-three and thirty-four for example. Keep reading to learn everything about the lcm (33,34) and the terms related to it.

What is the Least Common Multiple of 33 and 34?

If you just want to know what is the least common multiple of 33 and 34, it is 1122. Usually, this is written as

lcm(33,34) = 1122


The lcm of 33 and 34 can be obtained like this:
  • The multiples of 33 are … , 1089, 1122, 1155, ….
  • The multiples of 34 are …, 1088, 1122, 1156, …
  • The common multiples of 33 and 34 are n x 1122, intersecting the two sets above, .
  • In the intersection multiples of 33 ∩ multiples of 34 the least positive element is 1122.
  • Therefore, the least common multiple of 33 and 34 is 1122.

Taking the above into account you also know how to find all the common multiples of 33 and 34, not just the smallest. In the next section we show you how to calculate the lcm of thirty-three and thirty-four by means of two more methods.

How to find the LCM of 33 and 34

The least common multiple of 33 and 34 can be computed by using the greatest common factor aka gcf of 33 and 34. This is the easiest approach:

lcm (33,34) = = 1122



Alternatively, the lcm of 33 and 34 can be found using the prime factorization of 33 and 34:
  • The prime factorization of 33 is: 3 x 11
  • The prime factorization of 34 is: 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(33,33) = 1122

In any case, the easiest way to compute the result for two numbers like 33 and 34 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 33,342,2. 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 33 and 34

What is the least common multiple of 33 and 34 used for? Answer: It is helpful for adding and subtracting fractions like 1/33 and 1/34. Just multiply the dividends and divisors by 34 and 33, respectively, such that the divisors have the value of 1122, the lcm of 33 and 34.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 33 and 34

The most important properties of the lcm(33,34) are:

  • Commutative property: lcm(33,34) = lcm(34,33)
  • Associative property: lcm(33,34,n) = lcm(lcm(34,33),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-three / thirty-four 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