Given Numbers are 101, 109

We can find the LCM of 101, 109 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 101 and 109

Multiples of 101 =101,202,303,404,505,606,707,808,909,1010,1111,1212,1313,1414,1515,1616,1717,

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 101, 109 which is 11009

So, the LCM of 101, 109 is 11009.

One method for determining the LCM of 101 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 101's prime factorization:

Prime factors of 101 are 101.

101 = 101¹

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:101,109

101¹×109¹ = 11009

This shows that the LCM of 101 and 109 is 11009.

The first step in determining the Least Common Multiple of 101 and 109 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 101 and 109:

Lets look at the first ten multiples of these numbers, 101 and 109:

101,202,303,404,505,606,707,808,909,1717 are the first ten multiples of 101.

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 101 and 109, for example, are 1212, 1717, and 1744. 11009 is the least common multiple since it is the smallest.

101 and 109 have an LCM of 11009.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 101 and 109, than apply into the LCM equation.

GCF(101,109) = 1
LCM(101,109) = ( 101 × 109) / 1
LCM(101,109) = 11009 / 1
LCM(101,109) = 11009

1. What is the LCM of 101 and 109?

The LCM of 101 and 109 is 11009.

2. How to find the lowest common multiple of 101 and 109?

To find the lowest common multiple of 101 and 109, we have to get the multip;es of both numbers and identify the least common multiple in them which is 11009.

3. What are the Factors of 101?

Answer: Factors of 101 are 1, 101. There are 2 integers that are factors of 101. The greatest factor of 101 is 101.

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 101 and 109 = 11009

Step 1: Find the prime factorization of 101

101 = 101

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 = 11009 = 101 x 109

Step 4: Therefore, the least common multiple of 101 and 109 is 11009.