The **lcm of 6 and 77** is the smallest positive integer that divides the numbers 6 and 77 without a remainder. Spelled out, it is the least common multiple of 6 and 77. Here you can find the lcm of 6 and 77, along with a total of three methods for computing it.

462

## What is the LCM of 6 and 77

If you just want to know *what is the least common multiple of 6 and 77*, it is **462**. Usually, this is written as

**lcm(6,77) = 462**

The lcm of 6 and 77 can be obtained like this:

- The multiples of 6 are … , 456, 462, 468, ….
- The multiples of 77 are …, 385, 462, 539, …
- The
*common*multiples of 6 and 77 are n x 462, intersecting the two sets above,. - In the intersection multiples of 6 ∩ multiples of 77 the
*least*positive element is 462. - Therefore, the
**least common multiple of 6 and 77 is 462**.

Taking the above into account you also know how to find *all* the common multiples of 6 and 77, not just the smallest. In the next section we show you how to calculate the lcm of six and seventy-seven by means of two more methods.

## How to find the LCM of 6 and 77

The least common multiple of 6 and 77 can be computed by using the greatest common factor aka gcf of 6 and 77. This is the easiest approach:

Alternatively, the lcm of 6 and 77 can be found using the prime factorization of 6 and 77:

- The prime factorization of 6 is: 2 x 3
- The prime factorization of 77 is: 7 x 11
- Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(6,6) = 462

In any case, the easiest way to compute the lcm of two numbers like 6 and 77 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 6,77. Push the button only to start over.

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## Use of LCM of 6 and 77

What is the least common multiple of 6 and 77 used for? Answer: It is helpful for adding and subtracting fractions like 1/6 and 1/77. Just multiply the dividends and divisors by 77 and 6, respectively, such that the divisors have the value of 462, the lcm of 6 and 77.

## Properties of LCM of 6 and 77

The most important properties of the lcm(6,77) are:

- Commutative property: lcm(6,77) = lcm(77,6)
- Associative property: lcm(6,77,n) = lcm(lcm(77,6),n)

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 6 and 77 is 462. In common notation: lcm (6,77) = 462.

If you have been searching for lcm 6 and 77 or lcm 6 77 then you have come to the correct page, too. The same is the true if you typed lcm for 6 and 77 in your favorite search engine.

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

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