LCM of 176 and 180
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 176 and 180 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 7920 as output. Here you can check the answer for Find the LCM of 176 and 180.
What is LCM of 176 and 180
Given Numbers are 176, 180
We can find the LCM of 176, 180 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 176 and 180
Multiples of 176 =176,352,528,704,880,1056,1232,1408,1584,1760,1936,2112,2288,2464,2640,2816,2992,
Multiples of 180 =180,360,540,720,900,1080,1260,1440,1620,1800,1980,2160,2340,2520,2700,2880,3060,
Now, get the least common multiple of 176, 180 which is 7920
So, the LCM of 176, 180 is 7920.
Least Common Multiple (LCM) of 176 and 180 with the help of Prime Factorisation
One method for determining the LCM of 176 and 180 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 176's prime factorization:
| 2 | 176 |
| 2 | 88 |
| 2 | 44 |
| 2 | 22 |
| 11 | 11 |
| 1 |
Prime factors of 176 are 2,11.
176 = 24×111
And this is 180's prime factorization:
| 2 | 180 |
| 2 | 90 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 180 are 2, 3,5.
180 = 22×32×51
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: 2,11, 3,5
.24×32×51×111 = 7920
This shows that the LCM of 176 and 180 is 7920.
How to Calculate the LCM of 176 and 180 Using Common Multiples
The first step in determining the Least Common Multiple of 176 and 180 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 176 and 180:
Lets look at the first ten multiples of these numbers, 176 and 180:
176,352,528,704,880,1056,1232,1408,1584,2992 are the first ten multiples of 176.
180,360,540,720,900,1080,1260,1440,1620,3060 are the first ten multiples of 180.
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 176 and 180, for example, are 2112, 2992, and 2880. 7920 is the least common multiple since it is the smallest.
176 and 180 have an LCM of 7920.
Least Common Multiple of 176 and 180 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 176 and 180, than apply into the LCM equation.
GCF(176,180) = 4
LCM(176,180) = ( 176 × 180) / 4
LCM(176,180) = 31680 / 4
LCM(176,180) = 7920
Related Least Common Multiples of 176
Related Least Common Multiples of 180
Frequently Asked Questions on LCM of 176 and 180
1. What is the LCM of 176 and 180?
The LCM of 176 and 180 is 7920.
2. How to find the lowest common multiple of 176 and 180?
To find the lowest common multiple of 176 and 180, we have to get the multip;es of both numbers and identify the least common multiple in them which is 7920.
3. What are the Factors of 176?
Answer: Factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176. There are 10 integers that are factors of 176. The greatest factor of 176 is 176.
4. What are the Factors of 180?
Answer: Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180. There are 18 integers that are factors of 180. The greatest factor of 180 is 180.
5. How to Find the LCM of 176 and 180?Answer:
Least Common Multiple of 176 and 180 = 7920
Step 1: Find the prime factorization of 176
176 = 2 x 2 x 2 x 2 x 11
Step 2: Find the prime factorization of 180
180 = 2 x 2 x 3 x 3 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 7920 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11
Step 4: Therefore, the least common multiple of 176 and 180 is 7920.