LCM of 114 and 120
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 114 and 120 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 2280 as output. Here you can check the answer for Find the LCM of 114 and 120.
What is LCM of 114 and 120
Given Numbers are 114, 120
We can find the LCM of 114, 120 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 114 and 120
Multiples of 114 =114,228,342,456,570,684,798,912,1026,1140,1254,1368,1482,1596,1710,1824,1938,
Multiples of 120 =120,240,360,480,600,720,840,960,1080,1200,1320,1440,1560,1680,1800,1920,2040,
Now, get the least common multiple of 114, 120 which is 2280
So, the LCM of 114, 120 is 2280.
Least Common Multiple (LCM) of 114 and 120 with the help of Prime Factorisation
One method for determining the LCM of 114 and 120 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 114's prime factorization:
| 2 | 114 |
| 3 | 57 |
| 19 | 19 |
| 1 |
Prime factors of 114 are 2, 3,19.
114 = 21×31×191
And this is 120's prime factorization:
| 2 | 120 |
| 2 | 60 |
| 2 | 30 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 120 are 2, 3,5.
120 = 23×31×51
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, 3,19,5
.23×31×51×191 = 2280
This shows that the LCM of 114 and 120 is 2280.
How to Calculate the LCM of 114 and 120 Using Common Multiples
The first step in determining the Least Common Multiple of 114 and 120 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 114 and 120:
Lets look at the first ten multiples of these numbers, 114 and 120:
114,228,342,456,570,684,798,912,1026,1938 are the first ten multiples of 114.
120,240,360,480,600,720,840,960,1080,2040 are the first ten multiples of 120.
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 114 and 120, for example, are 1368, 1938, and 1920. 2280 is the least common multiple since it is the smallest.
114 and 120 have an LCM of 2280.
Least Common Multiple of 114 and 120 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 114 and 120, than apply into the LCM equation.
GCF(114,120) = 6
LCM(114,120) = ( 114 × 120) / 6
LCM(114,120) = 13680 / 6
LCM(114,120) = 2280
Related Least Common Multiples of 114
Related Least Common Multiples of 120
Frequently Asked Questions on LCM of 114 and 120
1. What is the LCM of 114 and 120?
The LCM of 114 and 120 is 2280.
2. How to find the lowest common multiple of 114 and 120?
To find the lowest common multiple of 114 and 120, we have to get the multip;es of both numbers and identify the least common multiple in them which is 2280.
3. What are the Factors of 114?
Answer: Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. There are 8 integers that are factors of 114. The greatest factor of 114 is 114.
4. What are the Factors of 120?
Answer: Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. There are 16 integers that are factors of 120. The greatest factor of 120 is 120.
5. How to Find the LCM of 114 and 120?Answer:
Least Common Multiple of 114 and 120 = 2280
Step 1: Find the prime factorization of 114
114 = 2 x 3 x 19
Step 2: Find the prime factorization of 120
120 = 2 x 2 x 2 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 = 2280 = 2 x 2 x 2 x 3 x 5 x 19
Step 4: Therefore, the least common multiple of 114 and 120 is 2280.