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LCM of 36 and 70

The lcm of 36 and 70 is the smallest positive integer that divides the numbers 36 and 70 without a remainder. Spelled out, it is the least common multiple of 36 and 70. Here you can find the result for 36 and 70, along with a total of three methods for computing it.


1260

This Least Common Multiple Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 36 and 70, but also that of three or more integers including thirty-six and seventy for example. Keep reading to learn everything about the lcm (36,70) and the terms related to it.

What is the Least Common Multiple of 36 and 70?

If you just want to know what is the least common multiple of 36 and 70, it is 1260. Usually, this is written as

lcm(36,70) = 1260


The lcm of 36 and 70 can be obtained like this:
  • The multiples of 36 are … , 1224, 1260, 1296, ….
  • The multiples of 70 are …, 1190, 1260, 1330, …
  • The common multiples of 36 and 70 are n x 1260, intersecting the two sets above, .
  • In the intersection multiples of 36 ∩ multiples of 70 the least positive element is 1260.
  • Therefore, the least common multiple of 36 and 70 is 1260.

Taking the above into account you also know how to find all the common multiples of 36 and 70, not just the smallest. In the next section we show you how to calculate the lcm of thirty-six and seventy by means of two more methods.

How to find the LCM of 36 and 70

The least common multiple of 36 and 70 can be computed by using the greatest common factor aka gcf of 36 and 70. This is the easiest approach:

lcm (36,70) = = 1260



Alternatively, the lcm of 36 and 70 can be found using the prime factorization of 36 and 70:
  • The prime factorization of 36 is: 2 x 2 x 3 x 3
  • The prime factorization of 70 is: 2 x 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(36,36) = 1260

In any case, the easiest way to compute the result for two numbers like 36 and 70 is by using our calculator above. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 36,702,2. Push the button only to start over.

Similar searched terms on our site also include:

In the next paragraph we explain how the mathematical concept can be employed.

Keep reading – it’s really interesting.

Use of Least Common Multiple of 36 and 70

What is the least common multiple of 36 and 70 used for? Answer: It is helpful for adding and subtracting fractions like 1/36 and 1/70. Just multiply the dividends and divisors by 35 and 18, respectively, such that the divisors have the value of 1260, the lcm of 36 and 70.

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Next, we shed a light on the mathematical properties.

Properties of LCM of 36 and 70

The most important properties of the lcm(36,70) are:

  • Commutative property: lcm(36,70) = lcm(70,36)
  • Associative property: lcm(36,70,n) = lcm(lcm(70,36),n)

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

Summary

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

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– Article written by Mark, last updated on August 8th, 2023