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LCM of 67 and 45

The lcm of 67 and 45 is the smallest positive integer that divides the numbers 67 and 45 without a remainder. Spelled out, it is the least common multiple of 67 and 45. Here you can find the result for 67 and 45, along with a total of three methods for computing it.


3015

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 67 and 45, but also that of three or more integers including sixty-seven and forty-five for example. Keep reading to learn everything about the lcm (67,45) and the terms related to it.

What is the Least Common Multiple of 67 and 45?

If you just want to know what is the least common multiple of 67 and 45, it is 3015. Usually, this is written as

lcm(67,45) = 3015


The lcm of 67 and 45 can be obtained like this:
  • The multiples of 67 are … , 2948, 3015, 3082, ….
  • The multiples of 45 are …, 2970, 3015, 3060, …
  • The common multiples of 67 and 45 are n x 3015, intersecting the two sets above, .
  • In the intersection multiples of 67 ∩ multiples of 45 the least positive element is 3015.
  • Therefore, the least common multiple of 67 and 45 is 3015.

Taking the above into account you also know how to find all the common multiples of 67 and 45, not just the smallest. In the next section we show you how to calculate the lcm of sixty-seven and forty-five by means of two more methods.

How to find the LCM of 67 and 45

The least common multiple of 67 and 45 can be computed by using the greatest common factor aka gcf of 67 and 45. This is the easiest approach:

lcm (67,45) = = 3015



Alternatively, the lcm of 67 and 45 can be found using the prime factorization of 67 and 45:
  • The prime factorization of 67 is: 67
  • The prime factorization of 45 is: 3 x 3 x 5
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(67,67) = 3015

In any case, the easiest way to compute the result for two numbers like 67 and 45 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 67,452,2. 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 67 and 45

What is the least common multiple of 67 and 45 used for? Answer: It is helpful for adding and subtracting fractions like 1/67 and 1/45. Just multiply the dividends and divisors by 45 and 67, respectively, such that the divisors have the value of 3015, the lcm of 67 and 45.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 67 and 45

The most important properties of the lcm(67,45) are:

  • Commutative property: lcm(67,45) = lcm(45,67)
  • Associative property: lcm(67,45,n) = lcm(lcm(45,67),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 sixty-seven / forty-five 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