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LCM of 6 and 77

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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. In addition, we have a calculator you should check out. Not only can it determine the lcm of 6 and 77, but also that of three or more integers including six and seventy-seven for example. Keep reading to learn everything about the lcm (6,77) and the terms related to it.

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, n\neq 0 \thinspace\in\thinspace\mathbb{Z}.
  • 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:

lcm (6,77) = \frac{6 \times 77}{gcf(6,77)} = \frac{462}{1} = 462

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.

The lcm is...
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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.

\frac{1}{6} + \frac{1}{77} = \frac{77}{462} + \frac{6}{462} = \frac{83}{462}. \frac{1}{6} - \frac{1}{77} = \frac{77}{462} - \frac{6}{462} = \frac{71}{462}.

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) n\neq 0 \thinspace\in\thinspace\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 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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