LCM of 75 and 90


The lcm of 75 and 90 is the smallest positive integer that divides the numbers 75 and 90 without a remainder. Spelled out, it is the least common multiple of 75 and 90. Here you can find the lcm of 75 and 90, 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 75 and 90, but also that of three or more integers including seventy-five and ninety for example. Keep reading to learn everything about the lcm (75,90) and the terms related to it.

What is the LCM of 75 and 90

If you just want to know what is the least common multiple of 75 and 90, it is 450. Usually, this is written as

lcm(75,90) = 450

The lcm of 75 and 90 can be obtained like this:

  • The multiples of 75 are …, 375, 450, 525, ….
  • The multiples of 90 are …, 360, 450, 540, …
  • The common multiples of 75 and 90 are n x 450, intersecting the two sets above, $\hspace{3px}n \hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$.
  • In the intersection multiples of 75 ∩ multiples of 90 the least positive element is 450.
  • Therefore, the least common multiple of 75 and 90 is 450.

Taking the above into account you also know how to find all the common multiples of 75 and 90, not just the smallest. In the next section we show you how to calculate the lcm of seventy-five and ninety by means of two more methods.

How to find the LCM of 75 and 90

The least common multiple of 75 and 90 can be computed by using the greatest common factor aka gcf of 75 and 90. This is the easiest approach:

lcm (75,90) = $\frac{75 \times 90}{gcf(75,90)} = \frac{6750}{15}$ = 450

Alternatively, the lcm of 75 and 90 can be found using the prime factorization of 75 and 90:

  • The prime factorization of 75 is: 3 x 5 x 5
  • The prime factorization of 90 is: 2 x 3 x 3 x 5
  • Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(75,75) = 450

In any case, the easiest way to compute the lcm of two numbers like 75 and 90 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 75,90. Push the button only to start over.

The lcm is...
Similar searched terms on our site also include:

Use of LCM of 75 and 90

What is the least common multiple of 75 and 90 used for? Answer: It is helpful for adding and subtracting fractions like 1/75 and 1/90. Just multiply the dividends and divisors by 6 and 5, respectively, such that the divisors have the value of 450, the lcm of 75 and 90.

$\frac{1}{75} + \frac{1}{90} = \frac{6}{450} + \frac{5}{450} = \frac{11}{450}$. $\hspace{30px}\frac{1}{75} – \frac{1}{90} = \frac{6}{450} – \frac{5}{450} = \frac{1}{450}$.

Properties of LCM of 75 and 90

The most important properties of the lcm(75,90) are:

  • Commutative property: lcm(75,90) = lcm(90,75)
  • Associative property: lcm(75,90,n) = lcm(lcm(90,75),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 75 and 90 is 450. In common notation: lcm (75,90) = 450.

If you have been searching for lcm 75 and 90 or lcm 75 90 then you have come to the correct page, too. The same is the true if you typed lcm for 75 and 90 in your favorite search engine.

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

Questions and comments related to the lcm of 75 and 90 are really appreciated. Use the form below or send us a mail to get in touch.

Please hit the sharing buttons if our article about the least common multiple of 75 and 90 has been useful to you, and make sure to bookmark our site.

Thanks for your visit.

Print Friendly, PDF & Email
Posted in Least Common Multiple

Leave a Reply

Your email address will not be published. Required fields are marked *

*


Related pages


prime factorization for 8prime factorization of 113the prime factorization of 245find the prime factorization of 49times table 20x20the prime factorization of 175hcf of 72 and 967s times tablesthe prime factorization of 72what is the lcm of 10 and 5multiplication chart 1 150what is the least common multiple of 48 and 72prime factorization of 1000prime factorization of 350prime factorization of 432what is the lcm of 60 and 72multiplication chart 1 50 printableprime factor of 92what is the prime factorization of 126multiplication table 1-100 printableprime factorization of 162gcf of 96 and 144whats prime factorization147 prime numbergreatest common factor of 121is 141 a prime numberprime factorization chart 1-10097 prime factorization8x times tablewhat is the prime factorization of 330prime factorization 245prime factorization of 293what is the greatest common factor of 72 and 96prime factorization 96what is the gcf of 96 48 and 84prime factorization of 55common multiples of 3 and 5prime factorization of 110prime factorization of 725gcf of 45 and 75gcf of 81 and 48greatest common factor of 21 35 4948 as a product of prime factorsgcf of 64 and 48what is the gcf of 35 and 63multiplication table 90x90what is the gcf of 56 and 98common multiples of 4 and 10gcf of 81 and 48gcf of 45 and 75gcf of 81 and 48prime factorization 132list the prime factors of 42what is the prime factorization of 103find the prime factorization of 225prime factor of 91multiplication table up to 1000what are the prime factors of 65gcfcalculator40x timetable5x tableshcf of 45 and 72lowest common multiple of 60 and 96196 prime factorizationprime factorization of 297prime factorization 72what is the prime factorization of 2800multiplication table 30x30lcm 5 7greatest common factor of 27 and 54largest common denominator calculatorprime factors of numbers 1 100prime factorization of 880whats the prime factorization of 144prime factorization of 288whats a prime factormultiplication table up to 1000gcf of 81 and 36100-81