LCM of 168 and 175
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 168 and 175 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 4200 as output. Here you can check the answer for Find the LCM of 168 and 175.
What is LCM of 168 and 175
Given Numbers are 168, 175
We can find the LCM of 168, 175 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 168 and 175
Multiples of 168 =168,336,504,672,840,1008,1176,1344,1512,1680,1848,2016,2184,2352,2520,2688,2856,
Multiples of 175 =175,350,525,700,875,1050,1225,1400,1575,1750,1925,2100,2275,2450,2625,2800,2975,
Now, get the least common multiple of 168, 175 which is 4200
So, the LCM of 168, 175 is 4200.
Least Common Multiple (LCM) of 168 and 175 with the help of Prime Factorisation
One method for determining the LCM of 168 and 175 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 168's prime factorization:
| 2 | 168 |
| 2 | 84 |
| 2 | 42 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 168 are 2, 3,7.
168 = 23×31×71
And this is 175's prime factorization:
| 5 | 175 |
| 5 | 35 |
| 7 | 7 |
| 1 |
Prime factors of 175 are 5,7.
175 = 52×71
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, 3,7,5
.23×31×52×71 = 4200
This shows that the LCM of 168 and 175 is 4200.
How to Calculate the LCM of 168 and 175 Using Common Multiples
The first step in determining the Least Common Multiple of 168 and 175 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 168 and 175:
Lets look at the first ten multiples of these numbers, 168 and 175:
168,336,504,672,840,1008,1176,1344,1512,2856 are the first ten multiples of 168.
175,350,525,700,875,1050,1225,1400,1575,2975 are the first ten multiples of 175.
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 168 and 175, for example, are 2016, 2856, and 2800. 4200 is the least common multiple since it is the smallest.
168 and 175 have an LCM of 4200.
Least Common Multiple of 168 and 175 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 168 and 175, than apply into the LCM equation.
GCF(168,175) = 7
LCM(168,175) = ( 168 × 175) / 7
LCM(168,175) = 29400 / 7
LCM(168,175) = 4200
Related Least Common Multiples of 168
Related Least Common Multiples of 175
Frequently Asked Questions on LCM of 168 and 175
1. What is the LCM of 168 and 175?
The LCM of 168 and 175 is 4200.
2. How to find the lowest common multiple of 168 and 175?
To find the lowest common multiple of 168 and 175, we have to get the multip;es of both numbers and identify the least common multiple in them which is 4200.
3. What are the Factors of 168?
Answer: Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168. There are 16 integers that are factors of 168. The greatest factor of 168 is 168.
4. What are the Factors of 175?
Answer: Factors of 175 are 1, 5, 7, 25, 35, 175. There are 6 integers that are factors of 175. The greatest factor of 175 is 175.
5. How to Find the LCM of 168 and 175?Answer:
Least Common Multiple of 168 and 175 = 4200
Step 1: Find the prime factorization of 168
168 = 2 x 2 x 2 x 3 x 7
Step 2: Find the prime factorization of 175
175 = 5 x 5 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 = 4200 = 2 x 2 x 2 x 3 x 5 x 5 x 7
Step 4: Therefore, the least common multiple of 168 and 175 is 4200.