LCM of 34 and 33


The lcm of 34 and 33 is the smallest positive integer that divides the numbers 34 and 33 without a remainder. Spelled out, it is the least common multiple of 34 and 33. Here you can find the lcm of 34 and 33, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the lcm of 34 and 33, but also that of three or more integers including thirty-four and thirty-three for example. Keep reading to learn everything about the lcm (34,33) and the terms related to it.

What is the LCM of 34 and 33

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

lcm(34,33) = 1122

The lcm of 34 and 33 can be obtained like this:

  • The multiples of 34 are …, 1088, 1122, 1156, ….
  • The multiples of 33 are …, 1089, 1122, 1155, …
  • The common multiples of 34 and 33 are n x 1122, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 34 ∩ multiples of 33 the least positive element is 1122.
  • Therefore, the least common multiple of 34 and 33 is 1122.

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

How to find the LCM of 34 and 33

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

lcm (34,33) = $\frac{34 \times 33}{gcf(34,33)} = \frac{1122}{1}$ = 1122

Alternatively, the lcm of 34 and 33 can be found using the prime factorization of 34 and 33:

  • The prime factorization of 34 is: 2 x 17
  • The prime factorization of 33 is: 3 x 11
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(34,34) = 1122

In any case, the easiest way to compute the lcm of two numbers like 34 and 33 is by using our calculator below. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 34,33. Push the button only to start over.

The lcm is...
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Use of LCM of 34 and 33

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

$\frac{1}{34} + \frac{1}{33} = \frac{33}{1122} + \frac{34}{1122} = \frac{67}{1122}$. $\hspace{30px}\frac{1}{34} – \frac{1}{33} = \frac{33}{1122} – \frac{34}{1122} = \frac{-1}{1122}$.

Properties of LCM of 34 and 33

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

  • Commutative property: lcm(34,33) = lcm(33,34)
  • Associative property: lcm(34,33,n) = lcm(lcm(33,34),n) $\hspace{10px}n\neq 0 \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$

The associativity is particularly useful to get the lcm of three or more numbers; our calculator makes use of it.

To sum up, the lcm of 34 and 33 is 1122. In common notation: lcm (34,33) = 1122.

If you have been searching for lcm 34 and 33 or lcm 34 33 then you have come to the correct page, too. The same is the true if you typed lcm for 34 and 33 in your favorite search engine.

Note that you can find the least common multiple of many integer pairs including thirty-four / thirty-three by using the search form in the sidebar of this page.

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