LCM of 171 and 176
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 171 and 176 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 30096 as output. Here you can check the answer for Find the LCM of 171 and 176.
What is LCM of 171 and 176
Given Numbers are 171, 176
We can find the LCM of 171, 176 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 171 and 176
Multiples of 171 =171,342,513,684,855,1026,1197,1368,1539,1710,1881,2052,2223,2394,2565,2736,2907,
Multiples of 176 =176,352,528,704,880,1056,1232,1408,1584,1760,1936,2112,2288,2464,2640,2816,2992,
Now, get the least common multiple of 171, 176 which is 30096
So, the LCM of 171, 176 is 30096.
Least Common Multiple (LCM) of 171 and 176 with the help of Prime Factorisation
One method for determining the LCM of 171 and 176 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 171's prime factorization:
| 3 | 171 |
| 3 | 57 |
| 19 | 19 |
| 1 |
Prime factors of 171 are 3,19.
171 = 32×191
And this 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
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: 3,19, 2,11
.24×32×111×191 = 30096
This shows that the LCM of 171 and 176 is 30096.
How to Calculate the LCM of 171 and 176 Using Common Multiples
The first step in determining the Least Common Multiple of 171 and 176 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 171 and 176:
Lets look at the first ten multiples of these numbers, 171 and 176:
171,342,513,684,855,1026,1197,1368,1539,2907 are the first ten multiples of 171.
176,352,528,704,880,1056,1232,1408,1584,2992 are the first ten multiples of 176.
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 171 and 176, for example, are 2052, 2907, and 2816. 30096 is the least common multiple since it is the smallest.
171 and 176 have an LCM of 30096.
Least Common Multiple of 171 and 176 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 171 and 176, than apply into the LCM equation.
GCF(171,176) = 1
LCM(171,176) = ( 171 × 176) / 1
LCM(171,176) = 30096 / 1
LCM(171,176) = 30096
Related Least Common Multiples of 171
Related Least Common Multiples of 176
Frequently Asked Questions on LCM of 171 and 176
1. What is the LCM of 171 and 176?
The LCM of 171 and 176 is 30096.
2. How to find the lowest common multiple of 171 and 176?
To find the lowest common multiple of 171 and 176, we have to get the multip;es of both numbers and identify the least common multiple in them which is 30096.
3. What are the Factors of 171?
Answer: Factors of 171 are 1, 3, 9, 19, 57, 171. There are 6 integers that are factors of 171. The greatest factor of 171 is 171.
4. 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.
5. How to Find the LCM of 171 and 176?Answer:
Least Common Multiple of 171 and 176 = 30096
Step 1: Find the prime factorization of 171
171 = 3 x 3 x 19
Step 2: Find the prime factorization of 176
176 = 2 x 2 x 2 x 2 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 30096 = 2 x 2 x 2 x 2 x 3 x 3 x 11 x 19
Step 4: Therefore, the least common multiple of 171 and 176 is 30096.