LCM of 120 and 126
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 120 and 126 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 2520 as output. Here you can check the answer for Find the LCM of 120 and 126.
What is LCM of 120 and 126
Given Numbers are 120, 126
We can find the LCM of 120, 126 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 120 and 126
Multiples of 120 =120,240,360,480,600,720,840,960,1080,1200,1320,1440,1560,1680,1800,1920,2040,
Multiples of 126 =126,252,378,504,630,756,882,1008,1134,1260,1386,1512,1638,1764,1890,2016,2142,
Now, get the least common multiple of 120, 126 which is 2520
So, the LCM of 120, 126 is 2520.
Least Common Multiple (LCM) of 120 and 126 with the help of Prime Factorisation
One method for determining the LCM of 120 and 126 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 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
And this is 126's prime factorization:
| 2 | 126 |
| 3 | 63 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 126 are 2, 3,7.
126 = 21×32×71
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, 3,5,7
.23×32×51×71 = 2520
This shows that the LCM of 120 and 126 is 2520.
How to Calculate the LCM of 120 and 126 Using Common Multiples
The first step in determining the Least Common Multiple of 120 and 126 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 120 and 126:
Lets look at the first ten multiples of these numbers, 120 and 126:
120,240,360,480,600,720,840,960,1080,2040 are the first ten multiples of 120.
126,252,378,504,630,756,882,1008,1134,2142 are the first ten multiples of 126.
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 120 and 126, for example, are 1440, 2040, and 2016. 2520 is the least common multiple since it is the smallest.
120 and 126 have an LCM of 2520.
Least Common Multiple of 120 and 126 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 120 and 126, than apply into the LCM equation.
GCF(120,126) = 6
LCM(120,126) = ( 120 × 126) / 6
LCM(120,126) = 15120 / 6
LCM(120,126) = 2520
Related Least Common Multiples of 120
Related Least Common Multiples of 126
Frequently Asked Questions on LCM of 120 and 126
1. What is the LCM of 120 and 126?
The LCM of 120 and 126 is 2520.
2. How to find the lowest common multiple of 120 and 126?
To find the lowest common multiple of 120 and 126, we have to get the multip;es of both numbers and identify the least common multiple in them which is 2520.
3. 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.
4. What are the Factors of 126?
Answer: Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. There are 12 integers that are factors of 126. The greatest factor of 126 is 126.
5. How to Find the LCM of 120 and 126?Answer:
Least Common Multiple of 120 and 126 = 2520
Step 1: Find the prime factorization of 120
120 = 2 x 2 x 2 x 3 x 5
Step 2: Find the prime factorization of 126
126 = 2 x 3 x 3 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 = 2520 = 2 x 2 x 2 x 3 x 3 x 5 x 7
Step 4: Therefore, the least common multiple of 120 and 126 is 2520.