LCM of 123 and 128
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 123 and 128 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 15744 as output. Here you can check the answer for Find the LCM of 123 and 128.
What is LCM of 123 and 128
Given Numbers are 123, 128
We can find the LCM of 123, 128 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 123 and 128
Multiples of 123 =123,246,369,492,615,738,861,984,1107,1230,1353,1476,1599,1722,1845,1968,2091,
Multiples of 128 =128,256,384,512,640,768,896,1024,1152,1280,1408,1536,1664,1792,1920,2048,2176,
Now, get the least common multiple of 123, 128 which is 15744
So, the LCM of 123, 128 is 15744.
Least Common Multiple (LCM) of 123 and 128 with the help of Prime Factorisation
One method for determining the LCM of 123 and 128 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 123's prime factorization:
| 3 | 123 |
| 41 | 41 |
| 1 |
Prime factors of 123 are 3,41.
123 = 31×411
And this is 128's prime factorization:
| 2 | 128 |
| 2 | 64 |
| 2 | 32 |
| 2 | 16 |
| 2 | 8 |
| 2 | 4 |
| 2 | 2 |
| 1 |
Prime factors of 128 are 2.
128 = 27
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: 3,41,2
.27×31×411 = 15744
This shows that the LCM of 123 and 128 is 15744.
How to Calculate the LCM of 123 and 128 Using Common Multiples
The first step in determining the Least Common Multiple of 123 and 128 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 123 and 128:
Lets look at the first ten multiples of these numbers, 123 and 128:
123,246,369,492,615,738,861,984,1107,2091 are the first ten multiples of 123.
128,256,384,512,640,768,896,1024,1152,2176 are the first ten multiples of 128.
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 123 and 128, for example, are 1476, 2091, and 2048. 15744 is the least common multiple since it is the smallest.
123 and 128 have an LCM of 15744.
Least Common Multiple of 123 and 128 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 123 and 128, than apply into the LCM equation.
GCF(123,128) = 1
LCM(123,128) = ( 123 × 128) / 1
LCM(123,128) = 15744 / 1
LCM(123,128) = 15744
Related Least Common Multiples of 123
Related Least Common Multiples of 128
Frequently Asked Questions on LCM of 123 and 128
1. What is the LCM of 123 and 128?
The LCM of 123 and 128 is 15744.
2. How to find the lowest common multiple of 123 and 128?
To find the lowest common multiple of 123 and 128, we have to get the multip;es of both numbers and identify the least common multiple in them which is 15744.
3. What are the Factors of 123?
Answer: Factors of 123 are 1, 3, 41, 123. There are 4 integers that are factors of 123. The greatest factor of 123 is 123.
4. What are the Factors of 128?
Answer: Factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128. There are 8 integers that are factors of 128. The greatest factor of 128 is 128.
5. How to Find the LCM of 123 and 128?Answer:
Least Common Multiple of 123 and 128 = 15744
Step 1: Find the prime factorization of 123
123 = 3 x 41
Step 2: Find the prime factorization of 128
128 = 2 x 2 x 2 x 2 x 2 x 2 x 2
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 15744 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 41
Step 4: Therefore, the least common multiple of 123 and 128 is 15744.