LCM of 84 and 89
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 84 and 89 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 7476 as output. Here you can check the answer for Find the LCM of 84 and 89.
What is LCM of 84 and 89
Given Numbers are 84, 89
We can find the LCM of 84, 89 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 84 and 89
Multiples of 84 =84,168,252,336,420,504,588,672,756,840,924,1008,1092,1176,1260,1344,1428,
Multiples of 89 =89,178,267,356,445,534,623,712,801,890,979,1068,1157,1246,1335,1424,1513,
Now, get the least common multiple of 84, 89 which is 7476
So, the LCM of 84, 89 is 7476.
Least Common Multiple (LCM) of 84 and 89 with the help of Prime Factorisation
One method for determining the LCM of 84 and 89 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 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
And this is 89's prime factorization:
| 89 | 89 |
| 1 |
Prime factors of 89 are 89.
89 = 891
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: 2, 3,7,89
.22×31×71×891 = 7476
This shows that the LCM of 84 and 89 is 7476.
How to Calculate the LCM of 84 and 89 Using Common Multiples
The first step in determining the Least Common Multiple of 84 and 89 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 84 and 89:
Lets look at the first ten multiples of these numbers, 84 and 89:
84,168,252,336,420,504,588,672,756,1428 are the first ten multiples of 84.
89,178,267,356,445,534,623,712,801,1513 are the first ten multiples of 89.
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 84 and 89, for example, are 1008, 1428, and 1424. 7476 is the least common multiple since it is the smallest.
84 and 89 have an LCM of 7476.
Least Common Multiple of 84 and 89 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 84 and 89, than apply into the LCM equation.
GCF(84,89) = 1
LCM(84,89) = ( 84 × 89) / 1
LCM(84,89) = 7476 / 1
LCM(84,89) = 7476
Related Least Common Multiples of 84
Related Least Common Multiples of 89
Frequently Asked Questions on LCM of 84 and 89
1. What is the LCM of 84 and 89?
The LCM of 84 and 89 is 7476.
2. How to find the lowest common multiple of 84 and 89?
To find the lowest common multiple of 84 and 89, we have to get the multip;es of both numbers and identify the least common multiple in them which is 7476.
3. 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.
4. What are the Factors of 89?
Answer: Factors of 89 are 1, 89. There are 2 integers that are factors of 89. The greatest factor of 89 is 89.
5. How to Find the LCM of 84 and 89?Answer:
Least Common Multiple of 84 and 89 = 7476
Step 1: Find the prime factorization of 84
84 = 2 x 2 x 3 x 7
Step 2: Find the prime factorization of 89
89 = 89
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 7476 = 2 x 2 x 3 x 7 x 89
Step 4: Therefore, the least common multiple of 84 and 89 is 7476.