LCM of 28 and 34
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 28 and 34 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 476 as output. Here you can check the answer for Find the LCM of 28 and 34.
What is LCM of 28 and 34
Given Numbers are 28, 34
We can find the LCM of 28, 34 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 28 and 34
Multiples of 28 =28,56,84,112,140,168,196,224,252,280,308,336,364,392,420,448,476,
Multiples of 34 =34,68,102,136,170,204,238,272,306,340,374,408,442,476,510,544,578,
Now, get the least common multiple of 28, 34 which is 476
So, the LCM of 28, 34 is 476.
Least Common Multiple (LCM) of 28 and 34 with the help of Prime Factorisation
One method for determining the LCM of 28 and 34 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 28's prime factorization:
| 2 | 28 |
| 2 | 14 |
| 7 | 7 |
| 1 |
Prime factors of 28 are 2,7.
28 = 22×71
And this is 34's prime factorization:
| 2 | 34 |
| 17 | 17 |
| 1 |
Prime factors of 34 are 2,17.
34 = 21×171
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: 2,7,17
.22×71×171 = 476
This shows that the LCM of 28 and 34 is 476.
How to Calculate the LCM of 28 and 34 Using Common Multiples
The first step in determining the Least Common Multiple of 28 and 34 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 28 and 34:
Lets look at the first ten multiples of these numbers, 28 and 34:
28,56,84,112,140,168,196,224,252,476 are the first ten multiples of 28.
34,68,102,136,170,204,238,272,306,578 are the first ten multiples of 34.
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 28 and 34, for example, are 336, 476, and 544. 476 is the least common multiple since it is the smallest.
28 and 34 have an LCM of 476.
Least Common Multiple of 28 and 34 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 28 and 34, than apply into the LCM equation.
GCF(28,34) = 2
LCM(28,34) = ( 28 × 34) / 2
LCM(28,34) = 952 / 2
LCM(28,34) = 476
Related Least Common Multiples of 28
Related Least Common Multiples of 34
Frequently Asked Questions on LCM of 28 and 34
1. What is the LCM of 28 and 34?
The LCM of 28 and 34 is 476.
2. How to find the lowest common multiple of 28 and 34?
To find the lowest common multiple of 28 and 34, we have to get the multip;es of both numbers and identify the least common multiple in them which is 476.
3. What are the Factors of 28?
Answer: Factors of 28 are 1, 2, 4, 7, 14, 28. There are 6 integers that are factors of 28. The greatest factor of 28 is 28.
4. What are the Factors of 34?
Answer: Factors of 34 are 1, 2, 17, 34. There are 4 integers that are factors of 34. The greatest factor of 34 is 34.
5. How to Find the LCM of 28 and 34?Answer:
Least Common Multiple of 28 and 34 = 476
Step 1: Find the prime factorization of 28
28 = 2 x 2 x 7
Step 2: Find the prime factorization of 34
34 = 2 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 476 = 2 x 2 x 7 x 17
Step 4: Therefore, the least common multiple of 28 and 34 is 476.