# LCM of 33 and 61

The lcm of 33 and 61 is the smallest positive integer that divides the numbers 33 and 61 without a remainder. Spelled out, it is the least common multiple of 33 and 61. Here you can find the lcm of 33 and 61, 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 33 and 61, but also that of three or more integers including thirty-three and sixty-one for example. Keep reading to learn everything about the lcm (33,61) and the terms related to it.

## What is the LCM of 33 and 61

If you just want to know what is the least common multiple of 33 and 61, it is 2013. Usually, this is written as

lcm(33,61) = 2013

The lcm of 33 and 61 can be obtained like this:

• The multiples of 33 are … , 1980, 2013, 2046, ….
• The multiples of 61 are …, 1952, 2013, 2074, …
• The common multiples of 33 and 61 are n x 2013, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
• In the intersection multiples of 33 ∩ multiples of 61 the least positive element is 2013.
• Therefore, the least common multiple of 33 and 61 is 2013.

Taking the above into account you also know how to find all the common multiples of 33 and 61, not just the smallest. In the next section we show you how to calculate the lcm of thirty-three and sixty-one by means of two more methods.

## How to find the LCM of 33 and 61

The least common multiple of 33 and 61 can be computed by using the greatest common factor aka gcf of 33 and 61. This is the easiest approach:

lcm (33,61) = $\frac{33 \times 61}{gcf(33,61)} = \frac{2013}{1}$ = 2013

Alternatively, the lcm of 33 and 61 can be found using the prime factorization of 33 and 61:

• The prime factorization of 33 is: 3 x 11
• The prime factorization of 61 is: 61
• Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(33,33) = 2013

In any case, the easiest way to compute the lcm of two numbers like 33 and 61 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 33,61. Push the button only to start over.

The lcm is...
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## Use of LCM of 33 and 61

What is the least common multiple of 33 and 61 used for? Answer: It is helpful for adding and subtracting fractions like 1/33 and 1/61. Just multiply the dividends and divisors by 61 and 33, respectively, such that the divisors have the value of 2013, the lcm of 33 and 61.

$\frac{1}{33} + \frac{1}{61} = \frac{61}{2013} + \frac{33}{2013} = \frac{94}{2013}$. $\hspace{30px}\frac{1}{33} – \frac{1}{61} = \frac{61}{2013} – \frac{33}{2013} = \frac{28}{2013}$.

## Properties of LCM of 33 and 61

The most important properties of the lcm(33,61) are:

• Commutative property: lcm(33,61) = lcm(61,33)
• Associative property: lcm(33,61,n) = lcm(lcm(61,33),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 33 and 61 is 2013. In common notation: lcm (33,61) = 2013.

If you have been searching for lcm 33 and 61 or lcm 33 61 then you have come to the correct page, too. The same is the true if you typed lcm for 33 and 61 in your favorite search engine.

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

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