It is easy to find the LCM of 81 and 84 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 2268 as output. Here you can check the answer for Find the LCM of 81 and 84.
Given Numbers are 81, 84
We can find the LCM of 81, 84 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 81 and 84
Multiples of 81 =81,162,243,324,405,486,567,648,729,810,891,972,1053,1134,1215,1296,1377,
Multiples of 84 =84,168,252,336,420,504,588,672,756,840,924,1008,1092,1176,1260,1344,1428,
Now, get the least common multiple of 81, 84 which is 2268
So, the LCM of 81, 84 is 2268.
One method for determining the LCM of 81 and 84 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:
Here is 81's prime factorization:3 | 81 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 81 are 3.
81 = 34
And this is 84's prime factorization:
2 | 84 |
2 | 42 |
3 | 21 |
7 | 7 |
1 |
Prime factors of 84 are 2, 3,7.
84 = 22×31×71
When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered:3, 2,7
.22×34×71 = 2268
This shows that the LCM of 81 and 84 is 2268.
The first step in determining the Least Common Multiple of 81 and 84 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 81 and 84:
Lets look at the first ten multiples of these numbers, 81 and 84:
81,162,243,324,405,486,567,648,729,1377 are the first ten multiples of 81.
84,168,252,336,420,504,588,672,756,1428 are the first ten multiples of 84.
You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 81 and 84, for example, are 972, 1377, and 1344. 2268 is the least common multiple since it is the smallest.
81 and 84 have an LCM of 2268.
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 81 and 84, than apply into the LCM equation.
GCF(81,84) = 3
LCM(81,84) = ( 81 × 84) / 3
LCM(81,84) = 6804 / 3
LCM(81,84) = 2268
1. What is the LCM of 81 and 84?
The LCM of 81 and 84 is 2268.
2. How to find the lowest common multiple of 81 and 84?
To find the lowest common multiple of 81 and 84, we have to get the multip;es of both numbers and identify the least common multiple in them which is 2268.
3. What are the Factors of 81?
Answer: Factors of 81 are 1, 3, 9, 27, 81. There are 5 integers that are factors of 81. The greatest factor of 81 is 81.
4. What are the Factors of 84?
Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.
5. How to Find the LCM of 81 and 84?Answer:
Least Common Multiple of 81 and 84 = 2268
Step 1: Find the prime factorization of 81
81 = 3 x 3 x 3 x 3
Step 2: Find the prime factorization of 84
84 = 2 x 2 x 3 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2268 = 2 x 2 x 3 x 3 x 3 x 3 x 7
Step 4: Therefore, the least common multiple of 81 and 84 is 2268.