can any one give me LCM OF 31 and 81 with explanation
Answers
Answer:
2511
Step-by-step explanation:
LCM of 31 and 81
The lcm of 31 and 81 is the smallest positive integer that divides the numbers 31 and 81 without a remainder. Spelled out, it is the least common multiple of 31 and 81. Here you can find the lcm of 31 and 81, 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 31 and 81, but also that of three or more integers including thirty-one and eighty-one for example. Keep reading to learn everything about the lcm (31,81) and the terms related to it.
What is the LCM of 31 and 81
If you just want to know what is the least common multiple of 31 and 81, it is 2511. Usually, this is written as
lcm(31,81) = 2511
The lcm of 31 and 81 can be obtained like this:
The multiples of 31 are … , 2480, 2511, 2542, ….
The multiples of 81 are …, 2430, 2511, 2592, …
The common multiples of 31 and 81 are n x 2511, intersecting the two sets above, n\neq 0 \thinspace\epsilon\thinspace\mathbb{Z}n
=0ϵZ.
In the intersection multiples of 31 ∩ multiples of 81 the least positive element is 2511.
Therefore, the least common multiple of 31 and 81 is 2511.
Taking the above into account you also know how to find all the common multiples of 31 and 81, not just the smallest. In the next section we show you how to calculate the lcm of thirty-one and eighty-one by means of two more methods.
How to find the LCM of 31 and 81
The least common multiple of 31 and 81 can be computed by using the greatest common factor aka gcf of 31 and 81. This is the easiest approach:
lcm (31,81) = \frac{31 \times 81}{gcf(31,81)} = \frac{2511}{1}
gcf(31,81)
31×81
=
1
2511
= 2511
Alternatively, the lcm of 31 and 81 can be found using the prime factorization of 31 and 81:
The prime factorization of 31 is: 31
The prime factorization of 81 is: 3 x 3 x 3 x 3
Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(31,31) = 2511
In any case, the easiest way to compute the lcm of two numbers like 31 and 81 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 31,81. Push the button only to start over.
Answer:
3 (31, 81
3 (31 , 27
3 (31, 9
3 (31, 3
31 ( 31, 1
11
⇢ 3 × 3 × 3 × 3 × 31
⇢ 2511