LCM of 184 and 189
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 184 and 189 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 34776 as output. Here you can check the answer for Find the LCM of 184 and 189.
What is LCM of 184 and 189
Given Numbers are 184, 189
We can find the LCM of 184, 189 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 184 and 189
Multiples of 184 =184,368,552,736,920,1104,1288,1472,1656,1840,2024,2208,2392,2576,2760,2944,3128,
Multiples of 189 =189,378,567,756,945,1134,1323,1512,1701,1890,2079,2268,2457,2646,2835,3024,3213,
Now, get the least common multiple of 184, 189 which is 34776
So, the LCM of 184, 189 is 34776.
Least Common Multiple (LCM) of 184 and 189 with the help of Prime Factorisation
One method for determining the LCM of 184 and 189 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 184's prime factorization:
| 2 | 184 |
| 2 | 92 |
| 2 | 46 |
| 23 | 23 |
| 1 |
Prime factors of 184 are 2,23.
184 = 23×231
And this is 189's prime factorization:
| 3 | 189 |
| 3 | 63 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 189 are 3,7.
189 = 33×71
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: 2,23, 3,7
.23×33×71×231 = 34776
This shows that the LCM of 184 and 189 is 34776.
How to Calculate the LCM of 184 and 189 Using Common Multiples
The first step in determining the Least Common Multiple of 184 and 189 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 184 and 189:
Lets look at the first ten multiples of these numbers, 184 and 189:
184,368,552,736,920,1104,1288,1472,1656,3128 are the first ten multiples of 184.
189,378,567,756,945,1134,1323,1512,1701,3213 are the first ten multiples of 189.
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 184 and 189, for example, are 2208, 3128, and 3024. 34776 is the least common multiple since it is the smallest.
184 and 189 have an LCM of 34776.
Least Common Multiple of 184 and 189 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 184 and 189, than apply into the LCM equation.
GCF(184,189) = 1
LCM(184,189) = ( 184 × 189) / 1
LCM(184,189) = 34776 / 1
LCM(184,189) = 34776
Related Least Common Multiples of 184
Related Least Common Multiples of 189
Frequently Asked Questions on LCM of 184 and 189
1. What is the LCM of 184 and 189?
The LCM of 184 and 189 is 34776.
2. How to find the lowest common multiple of 184 and 189?
To find the lowest common multiple of 184 and 189, we have to get the multip;es of both numbers and identify the least common multiple in them which is 34776.
3. What are the Factors of 184?
Answer: Factors of 184 are 1, 2, 4, 8, 23, 46, 92, 184. There are 8 integers that are factors of 184. The greatest factor of 184 is 184.
4. What are the Factors of 189?
Answer: Factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189. There are 8 integers that are factors of 189. The greatest factor of 189 is 189.
5. How to Find the LCM of 184 and 189?Answer:
Least Common Multiple of 184 and 189 = 34776
Step 1: Find the prime factorization of 184
184 = 2 x 2 x 2 x 23
Step 2: Find the prime factorization of 189
189 = 3 x 3 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 = 34776 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 23
Step 4: Therefore, the least common multiple of 184 and 189 is 34776.