LCM of 70 and 75


The lcm of 70 and 75 is the smallest positive integer that divides the numbers 70 and 75 without a remainder. Spelled out, it is the least common multiple of 70 and 75. Here you can find the lcm of 70 and 75, 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 70 and 75, but also that of three or more integers including seventy and seventy-five for example. Keep reading to learn everything about the lcm (70,75) and the terms related to it.

What is the LCM of 70 and 75

If you just want to know what is the least common multiple of 70 and 75, it is 1050. Usually, this is written as

lcm(70,75) = 1050

The lcm of 70 and 75 can be obtained like this:

  • The multiples of 70 are …, 980, 1050, 1120, ….
  • The multiples of 75 are …, 975, 1050, 1125, …
  • The common multiples of 70 and 75 are n x 1050, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 70 ∩ multiples of 75 the least positive element is 1050.
  • Therefore, the least common multiple of 70 and 75 is 1050.

Taking the above into account you also know how to find all the common multiples of 70 and 75, not just the smallest. In the next section we show you how to calculate the lcm of seventy and seventy-five by means of two more methods.

How to find the LCM of 70 and 75

The least common multiple of 70 and 75 can be computed by using the greatest common factor aka gcf of 70 and 75. This is the easiest approach:

lcm (70,75) = $\frac{70 \times 75}{gcf(70,75)} = \frac{5250}{5}$ = 1050

Alternatively, the lcm of 70 and 75 can be found using the prime factorization of 70 and 75:

  • The prime factorization of 70 is: 2 x 5 x 7
  • The prime factorization of 75 is: 3 x 5 x 5
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(70,70) = 1050

In any case, the easiest way to compute the lcm of two numbers like 70 and 75 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 70,75. Push the button only to start over.

The lcm is...
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Use of LCM of 70 and 75

What is the least common multiple of 70 and 75 used for? Answer: It is helpful for adding and subtracting fractions like 1/70 and 1/75. Just multiply the dividends and divisors by 15 and 14, respectively, such that the divisors have the value of 1050, the lcm of 70 and 75.

$\frac{1}{70} + \frac{1}{75} = \frac{15}{1050} + \frac{14}{1050} = \frac{29}{1050}$. $\hspace{30px}\frac{1}{70} – \frac{1}{75} = \frac{15}{1050} – \frac{14}{1050} = \frac{1}{1050}$.

Properties of LCM of 70 and 75

The most important properties of the lcm(70,75) are:

  • Commutative property: lcm(70,75) = lcm(75,70)
  • Associative property: lcm(70,75,n) = lcm(lcm(75,70),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 70 and 75 is 1050. In common notation: lcm (70,75) = 1050.

If you have been searching for lcm 70 and 75 or lcm 70 75 then you have come to the correct page, too. The same is the true if you typed lcm for 70 and 75 in your favorite search engine.

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

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