Given Numbers are 103, 109

We can find the LCM of 103, 109 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 103 and 109

Multiples of 103 =103,206,309,412,515,618,721,824,927,1030,1133,1236,1339,1442,1545,1648,1751,

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 103, 109 which is 11227

So, the LCM of 103, 109 is 11227.

One method for determining the LCM of 103 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 103's prime factorization:

Prime factors of 103 are 103.

103 = 103¹

And this is 109's prime factorization:

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:103,109

103¹×109¹ = 11227

This shows that the LCM of 103 and 109 is 11227.

The first step in determining the Least Common Multiple of 103 and 109 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 103 and 109:

Lets look at the first ten multiples of these numbers, 103 and 109:

103,206,309,412,515,618,721,824,927,1751 are the first ten multiples of 103.

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 103 and 109, for example, are 1236, 1751, and 1744. 11227 is the least common multiple since it is the smallest.

103 and 109 have an LCM of 11227.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 103 and 109, than apply into the LCM equation.

GCF(103,109) = 1
LCM(103,109) = ( 103 × 109) / 1
LCM(103,109) = 11227 / 1
LCM(103,109) = 11227

1. What is the LCM of 103 and 109?

The LCM of 103 and 109 is 11227.

2. How to find the lowest common multiple of 103 and 109?

To find the lowest common multiple of 103 and 109, we have to get the multip;es of both numbers and identify the least common multiple in them which is 11227.

3. What are the Factors of 103?

Answer: Factors of 103 are 1, 103. There are 2 integers that are factors of 103. The greatest factor of 103 is 103.

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.

Answer:

Least Common Multiple of 103 and 109 = 11227

Step 1: Find the prime factorization of 103

103 = 103

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 = 11227 = 103 x 109

Step 4: Therefore, the least common multiple of 103 and 109 is 11227.