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LCM of 24 and 35

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The lcm of 24 and 35 is the smallest positive integer that divides the numbers 24 and 35 without a remainder. Spelled out, it is the least common multiple of 24 and 35. Here you can find the lcm of 24 and 35, 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 24 and 35, but also that of three or more integers including twenty-four and thirty-five for example. Keep reading to learn everything about the lcm (24,35) and the terms related to it.

What is the LCM of 24 and 35

If you just want to know what is the least common multiple of 24 and 35, it is 840. Usually, this is written as

lcm(24,35) = 840

The lcm of 24 and 35 can be obtained like this:

  • The multiples of 24 are … , 816, 840, 864, ….
  • The multiples of 35 are …, 805, 840, 875, …
  • The common multiples of 24 and 35 are n x 840, intersecting the two sets above, n\neq 0 \thinspace\in\thinspace\mathbb{Z}.
  • In the intersection multiples of 24 ∩ multiples of 35 the least positive element is 840.
  • Therefore, the least common multiple of 24 and 35 is 840.

Taking the above into account you also know how to find all the common multiples of 24 and 35, not just the smallest. In the next section we show you how to calculate the lcm of twenty-four and thirty-five by means of two more methods.

How to find the LCM of 24 and 35

The least common multiple of 24 and 35 can be computed by using the greatest common factor aka gcf of 24 and 35. This is the easiest approach:

lcm (24,35) = \frac{24 \times 35}{gcf(24,35)} = \frac{840}{1} = 840

Alternatively, the lcm of 24 and 35 can be found using the prime factorization of 24 and 35:

  • The prime factorization of 24 is: 2 x 2 x 2 x 3
  • The prime factorization of 35 is: 5 x 7
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(24,24) = 840

In any case, the easiest way to compute the lcm of two numbers like 24 and 35 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 24,35. Push the button only to start over.

The lcm is...
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Use of LCM of 24 and 35

What is the least common multiple of 24 and 35 used for? Answer: It is helpful for adding and subtracting fractions like 1/24 and 1/35. Just multiply the dividends and divisors by 35 and 24, respectively, such that the divisors have the value of 840, the lcm of 24 and 35.

\frac{1}{24} + \frac{1}{35} = \frac{35}{840} + \frac{24}{840} = \frac{59}{840}. \frac{1}{24} - \frac{1}{35} = \frac{35}{840} - \frac{24}{840} = \frac{11}{840}.

Properties of LCM of 24 and 35

The most important properties of the lcm(24,35) are:

  • Commutative property: lcm(24,35) = lcm(35,24)
  • Associative property: lcm(24,35,n) = lcm(lcm(35,24),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 24 and 35 is 840. In common notation: lcm (24,35) = 840.

If you have been searching for lcm 24 and 35 or lcm 24 35 then you have come to the correct page, too. The same is the true if you typed lcm for 24 and 35 in your favorite search engine.

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

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