LCM of 102 and 106
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 102 and 106 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 5406 as output. Here you can check the answer for Find the LCM of 102 and 106.
What is LCM of 102 and 106
Given Numbers are 102, 106
We can find the LCM of 102, 106 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 102 and 106
Multiples of 102 =102,204,306,408,510,612,714,816,918,1020,1122,1224,1326,1428,1530,1632,1734,
Multiples of 106 =106,212,318,424,530,636,742,848,954,1060,1166,1272,1378,1484,1590,1696,1802,
Now, get the least common multiple of 102, 106 which is 5406
So, the LCM of 102, 106 is 5406.
Least Common Multiple (LCM) of 102 and 106 with the help of Prime Factorisation
One method for determining the LCM of 102 and 106 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 102's prime factorization:
| 2 | 102 |
| 3 | 51 |
| 17 | 17 |
| 1 |
Prime factors of 102 are 2, 3,17.
102 = 21×31×171
And this is 106's prime factorization:
| 2 | 106 |
| 53 | 53 |
| 1 |
Prime factors of 106 are 2,53.
106 = 21×531
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, 3,17,53
.21×31×171×531 = 5406
This shows that the LCM of 102 and 106 is 5406.
How to Calculate the LCM of 102 and 106 Using Common Multiples
The first step in determining the Least Common Multiple of 102 and 106 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 102 and 106:
Lets look at the first ten multiples of these numbers, 102 and 106:
102,204,306,408,510,612,714,816,918,1734 are the first ten multiples of 102.
106,212,318,424,530,636,742,848,954,1802 are the first ten multiples of 106.
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 102 and 106, for example, are 1224, 1734, and 1696. 5406 is the least common multiple since it is the smallest.
102 and 106 have an LCM of 5406.
Least Common Multiple of 102 and 106 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 102 and 106, than apply into the LCM equation.
GCF(102,106) = 2
LCM(102,106) = ( 102 × 106) / 2
LCM(102,106) = 10812 / 2
LCM(102,106) = 5406
Related Least Common Multiples of 102
Related Least Common Multiples of 106
Frequently Asked Questions on LCM of 102 and 106
1. What is the LCM of 102 and 106?
The LCM of 102 and 106 is 5406.
2. How to find the lowest common multiple of 102 and 106?
To find the lowest common multiple of 102 and 106, we have to get the multip;es of both numbers and identify the least common multiple in them which is 5406.
3. What are the Factors of 102?
Answer: Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. There are 8 integers that are factors of 102. The greatest factor of 102 is 102.
4. What are the Factors of 106?
Answer: Factors of 106 are 1, 2, 53, 106. There are 4 integers that are factors of 106. The greatest factor of 106 is 106.
5. How to Find the LCM of 102 and 106?Answer:
Least Common Multiple of 102 and 106 = 5406
Step 1: Find the prime factorization of 102
102 = 2 x 3 x 17
Step 2: Find the prime factorization of 106
106 = 2 x 53
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 5406 = 2 x 3 x 17 x 53
Step 4: Therefore, the least common multiple of 102 and 106 is 5406.