LCM of 126 and 132
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 126 and 132 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 2772 as output. Here you can check the answer for Find the LCM of 126 and 132.
What is LCM of 126 and 132
Given Numbers are 126, 132
We can find the LCM of 126, 132 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 126 and 132
Multiples of 126 =126,252,378,504,630,756,882,1008,1134,1260,1386,1512,1638,1764,1890,2016,2142,
Multiples of 132 =132,264,396,528,660,792,924,1056,1188,1320,1452,1584,1716,1848,1980,2112,2244,
Now, get the least common multiple of 126, 132 which is 2772
So, the LCM of 126, 132 is 2772.
Least Common Multiple (LCM) of 126 and 132 with the help of Prime Factorisation
One method for determining the LCM of 126 and 132 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 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
And this is 132's prime factorization:
| 2 | 132 |
| 2 | 66 |
| 3 | 33 |
| 11 | 11 |
| 1 |
Prime factors of 132 are 2, 3,11.
132 = 22×31×111
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, 3,7,11
.22×32×71×111 = 2772
This shows that the LCM of 126 and 132 is 2772.
How to Calculate the LCM of 126 and 132 Using Common Multiples
The first step in determining the Least Common Multiple of 126 and 132 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 126 and 132:
Lets look at the first ten multiples of these numbers, 126 and 132:
126,252,378,504,630,756,882,1008,1134,2142 are the first ten multiples of 126.
132,264,396,528,660,792,924,1056,1188,2244 are the first ten multiples of 132.
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 126 and 132, for example, are 1512, 2142, and 2112. 2772 is the least common multiple since it is the smallest.
126 and 132 have an LCM of 2772.
Least Common Multiple of 126 and 132 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 126 and 132, than apply into the LCM equation.
GCF(126,132) = 6
LCM(126,132) = ( 126 × 132) / 6
LCM(126,132) = 16632 / 6
LCM(126,132) = 2772
Related Least Common Multiples of 126
Related Least Common Multiples of 132
Frequently Asked Questions on LCM of 126 and 132
1. What is the LCM of 126 and 132?
The LCM of 126 and 132 is 2772.
2. How to find the lowest common multiple of 126 and 132?
To find the lowest common multiple of 126 and 132, we have to get the multip;es of both numbers and identify the least common multiple in them which is 2772.
3. 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.
4. What are the Factors of 132?
Answer: Factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132. There are 12 integers that are factors of 132. The greatest factor of 132 is 132.
5. How to Find the LCM of 126 and 132?Answer:
Least Common Multiple of 126 and 132 = 2772
Step 1: Find the prime factorization of 126
126 = 2 x 3 x 3 x 7
Step 2: Find the prime factorization of 132
132 = 2 x 2 x 3 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2772 = 2 x 2 x 3 x 3 x 7 x 11
Step 4: Therefore, the least common multiple of 126 and 132 is 2772.