LCM of 105 and 109
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 105 and 109 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 11445 as output. Here you can check the answer for Find the LCM of 105 and 109.
What is LCM of 105 and 109
Given Numbers are 105, 109
We can find the LCM of 105, 109 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 105 and 109
Multiples of 105 =105,210,315,420,525,630,735,840,945,1050,1155,1260,1365,1470,1575,1680,1785,
Multiples of 109 =109,218,327,436,545,654,763,872,981,1090,1199,1308,1417,1526,1635,1744,1853,
Now, get the least common multiple of 105, 109 which is 11445
So, the LCM of 105, 109 is 11445.
Least Common Multiple (LCM) of 105 and 109 with the help of Prime Factorisation
One method for determining the LCM of 105 and 109 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 105's prime factorization:
| 3 | 105 |
| 5 | 35 |
| 7 | 7 |
| 1 |
Prime factors of 105 are 3, 5,7.
105 = 31×51×71
And this is 109's prime factorization:
| 109 | 109 |
| 1 |
Prime factors of 109 are 109.
109 = 1091
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, 5,7,109
.31×51×71×1091 = 11445
This shows that the LCM of 105 and 109 is 11445.
How to Calculate the LCM of 105 and 109 Using Common Multiples
The first step in determining the Least Common Multiple of 105 and 109 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 105 and 109:
Lets look at the first ten multiples of these numbers, 105 and 109:
105,210,315,420,525,630,735,840,945,1785 are the first ten multiples of 105.
109,218,327,436,545,654,763,872,981,1853 are the first ten multiples of 109.
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 105 and 109, for example, are 1260, 1785, and 1744. 11445 is the least common multiple since it is the smallest.
105 and 109 have an LCM of 11445.
Least Common Multiple of 105 and 109 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 105 and 109, than apply into the LCM equation.
GCF(105,109) = 1
LCM(105,109) = ( 105 × 109) / 1
LCM(105,109) = 11445 / 1
LCM(105,109) = 11445
Related Least Common Multiples of 105
Related Least Common Multiples of 109
Frequently Asked Questions on LCM of 105 and 109
1. What is the LCM of 105 and 109?
The LCM of 105 and 109 is 11445.
2. How to find the lowest common multiple of 105 and 109?
To find the lowest common multiple of 105 and 109, we have to get the multip;es of both numbers and identify the least common multiple in them which is 11445.
3. What are the Factors of 105?
Answer: Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. There are 8 integers that are factors of 105. The greatest factor of 105 is 105.
4. What are the Factors of 109?
Answer: Factors of 109 are 1, 109. There are 2 integers that are factors of 109. The greatest factor of 109 is 109.
5. How to Find the LCM of 105 and 109?Answer:
Least Common Multiple of 105 and 109 = 11445
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 2: Find the prime factorization of 109
109 = 109
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 11445 = 3 x 5 x 7 x 109
Step 4: Therefore, the least common multiple of 105 and 109 is 11445.