Given Numbers are 109, 115

We can find the LCM of 109, 115 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 109 and 115

Multiples of 109 =109,218,327,436,545,654,763,872,981,1090,1199,1308,1417,1526,1635,1744,1853,

Multiples of 115 =115,230,345,460,575,690,805,920,1035,1150,1265,1380,1495,1610,1725,1840,1955,

Now, get the least common multiple of 109, 115 which is 12535

So, the LCM of 109, 115 is 12535.

One method for determining the LCM of 109 and 115 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 109's prime factorization:

Prime factors of 109 are 109.

109 = 109¹

And this is 115's prime factorization:

Prime factors of 115 are 5,23.

115 = 5¹×23¹

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:109, 5,23

5¹×23¹×109¹ = 12535

This shows that the LCM of 109 and 115 is 12535.

The first step in determining the Least Common Multiple of 109 and 115 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 109 and 115:

Lets look at the first ten multiples of these numbers, 109 and 115:

109,218,327,436,545,654,763,872,981,1853 are the first ten multiples of 109.

115,230,345,460,575,690,805,920,1035,1955 are the first ten multiples of 115.

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 109 and 115, for example, are 1308, 1853, and 1840. 12535 is the least common multiple since it is the smallest.

109 and 115 have an LCM of 12535.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 109 and 115, than apply into the LCM equation.

GCF(109,115) = 1
LCM(109,115) = ( 109 × 115) / 1
LCM(109,115) = 12535 / 1
LCM(109,115) = 12535

1. What is the LCM of 109 and 115?

The LCM of 109 and 115 is 12535.

2. How to find the lowest common multiple of 109 and 115?

To find the lowest common multiple of 109 and 115, we have to get the multip;es of both numbers and identify the least common multiple in them which is 12535.

3. 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.

4. What are the Factors of 115?

Answer: Factors of 115 are 1, 5, 23, 115. There are 4 integers that are factors of 115. The greatest factor of 115 is 115.

Answer:

Least Common Multiple of 109 and 115 = 12535

Step 1: Find the prime factorization of 109

109 = 109

Step 2: Find the prime factorization of 115

115 = 5 x 23

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 12535 = 5 x 23 x 109

Step 4: Therefore, the least common multiple of 109 and 115 is 12535.