The lcm of 67 and 75 is the smallest positive integer that divides the numbers 67 and 75 without a remainder. Spelled out, it is the least common multiple of 67 and 75. Here you can find the lcm of 67 and 75, along with a total of three methods for computing it.
What is the LCM of 67 and 75
If you just want to know what is the least common multiple of 67 and 75, it is 5025. Usually, this is written as
The lcm of 67 and 75 can be obtained like this:
- The multiples of 67 are … , 4958, 5025, 5092, ….
- The multiples of 75 are …, 4950, 5025, 5100, …
- The common multiples of 67 and 75 are n x 5025, intersecting the two sets above,
- In the intersection multiples of 67 ∩ multiples of 75 the least positive element is 5025.
- Therefore, the least common multiple of 67 and 75 is 5025.
Taking the above into account you also know how to find all the common multiples of 67 and 75, not just the smallest. In the next section we show you how to calculate the lcm of sixty-seven and seventy-five by means of two more methods.
How to find the LCM of 67 and 75
The least common multiple of 67 and 75 can be computed by using the greatest common factor aka gcf of 67 and 75. This is the easiest approach:
Alternatively, the lcm of 67 and 75 can be found using the prime factorization of 67 and 75:
- The prime factorization of 67 is: 67
- 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(67,67) = 5025
In any case, the easiest way to compute the lcm of two numbers like 67 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 67,75. Push the button only to start over.
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Use of LCM of 67 and 75
What is the least common multiple of 67 and 75 used for? Answer: It is helpful for adding and subtracting fractions like 1/67 and 1/75. Just multiply the dividends and divisors by 75 and 67, respectively, such that the divisors have the value of 5025, the lcm of 67 and 75.
Properties of LCM of 67 and 75
The most important properties of the lcm(67,75) are:
- Commutative property: lcm(67,75) = lcm(75,67)
- Associative property: lcm(67,75,n) = lcm(lcm(75,67),n)
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 67 and 75 is 5025. In common notation: lcm (67,75) = 5025.
If you have been searching for lcm 67 and 75 or lcm 67 75 then you have come to the correct page, too. The same is the true if you typed lcm for 67 and 75 in your favorite search engine.
Note that you can find the least common multiple of many integer pairs including sixty-seven / seventy-five by using the search form in the sidebar of this page.
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