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LCM of 22 and 67

The lcm of 22 and 67 is the smallest positive integer that divides the numbers 22 and 67 without a remainder. Spelled out, it is the least common multiple of 22 and 67. Here you can find the result for 22 and 67, along with a total of three methods for computing it.


1474

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 22 and 67, but also that of three or more integers including twenty-two and sixty-seven for example. Keep reading to learn everything about the lcm (22,67) and the terms related to it.

What is the Least Common Multiple of 22 and 67?

If you just want to know what is the least common multiple of 22 and 67, it is 1474. Usually, this is written as

lcm(22,67) = 1474


The lcm of 22 and 67 can be obtained like this:
  • The multiples of 22 are … , 1452, 1474, 1496, ….
  • The multiples of 67 are …, 1407, 1474, 1541, …
  • The common multiples of 22 and 67 are n x 1474, intersecting the two sets above, .
  • In the intersection multiples of 22 ∩ multiples of 67 the least positive element is 1474.
  • Therefore, the least common multiple of 22 and 67 is 1474.

Taking the above into account you also know how to find all the common multiples of 22 and 67, not just the smallest. In the next section we show you how to calculate the lcm of twenty-two and sixty-seven by means of two more methods.

How to find the LCM of 22 and 67

The least common multiple of 22 and 67 can be computed by using the greatest common factor aka gcf of 22 and 67. This is the easiest approach:

lcm (22,67) = = 1474



Alternatively, the lcm of 22 and 67 can be found using the prime factorization of 22 and 67:
  • The prime factorization of 22 is: 2 x 11
  • The prime factorization of 67 is: 67
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(22,22) = 1474

In any case, the easiest way to compute the result for two numbers like 22 and 67 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 22,672,2. 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 22 and 67

What is the least common multiple of 22 and 67 used for? Answer: It is helpful for adding and subtracting fractions like 1/22 and 1/67. Just multiply the dividends and divisors by 67 and 22, respectively, such that the divisors have the value of 1474, the lcm of 22 and 67.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 22 and 67

The most important properties of the lcm(22,67) are:

  • Commutative property: lcm(22,67) = lcm(67,22)
  • Associative property: lcm(22,67,n) = lcm(lcm(67,22),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-two / sixty-seven 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