Given Numbers are 109, 113

We can find the LCM of 109, 113 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 109 and 113

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

Multiples of 113 =113,226,339,452,565,678,791,904,1017,1130,1243,1356,1469,1582,1695,1808,1921,

Now, get the least common multiple of 109, 113 which is 12317

So, the LCM of 109, 113 is 12317.

One method for determining the LCM of 109 and 113 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 113's prime factorization:

Prime factors of 113 are 113.

113 = 113¹

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:109,113

109¹×113¹ = 12317

This shows that the LCM of 109 and 113 is 12317.

The first step in determining the Least Common Multiple of 109 and 113 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 109 and 113:

Lets look at the first ten multiples of these numbers, 109 and 113:

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

113,226,339,452,565,678,791,904,1017,1921 are the first ten multiples of 113.

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 113, for example, are 1308, 1853, and 1808. 12317 is the least common multiple since it is the smallest.

109 and 113 have an LCM of 12317.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 109 and 113, than apply into the LCM equation.

GCF(109,113) = 1
LCM(109,113) = ( 109 × 113) / 1
LCM(109,113) = 12317 / 1
LCM(109,113) = 12317

1. What is the LCM of 109 and 113?

The LCM of 109 and 113 is 12317.

2. How to find the lowest common multiple of 109 and 113?

To find the lowest common multiple of 109 and 113, we have to get the multip;es of both numbers and identify the least common multiple in them which is 12317.

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 113?

Answer: Factors of 113 are 1, 113. There are 2 integers that are factors of 113. The greatest factor of 113 is 113.

Answer:

Least Common Multiple of 109 and 113 = 12317

Step 1: Find the prime factorization of 109

109 = 109

Step 2: Find the prime factorization of 113

113 = 113

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

LCM = 12317 = 109 x 113

Step 4: Therefore, the least common multiple of 109 and 113 is 12317.