Given Numbers are 102, 107

We can find the LCM of 102, 107 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 102 and 107

Multiples of 102 =102,204,306,408,510,612,714,816,918,1020,1122,1224,1326,1428,1530,1632,1734,

Multiples of 107 =107,214,321,428,535,642,749,856,963,1070,1177,1284,1391,1498,1605,1712,1819,

Now, get the least common multiple of 102, 107 which is 10914

So, the LCM of 102, 107 is 10914.

One method for determining the LCM of 102 and 107 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 102's prime factorization:

Prime factors of 102 are 2, 3,17.

102 = 2¹×3¹×17¹

And this is 107's prime factorization:

Prime factors of 107 are 107.

107 = 107¹

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: 2, 3,17,107

2¹×3¹×17¹×107¹ = 10914

This shows that the LCM of 102 and 107 is 10914.

The first step in determining the Least Common Multiple of 102 and 107 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 102 and 107:

Lets look at the first ten multiples of these numbers, 102 and 107:

102,204,306,408,510,612,714,816,918,1734 are the first ten multiples of 102.

107,214,321,428,535,642,749,856,963,1819 are the first ten multiples of 107.

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 102 and 107, for example, are 1224, 1734, and 1712. 10914 is the least common multiple since it is the smallest.

102 and 107 have an LCM of 10914.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 102 and 107, than apply into the LCM equation.

GCF(102,107) = 1
LCM(102,107) = ( 102 × 107) / 1
LCM(102,107) = 10914 / 1
LCM(102,107) = 10914

1. What is the LCM of 102 and 107?

The LCM of 102 and 107 is 10914.

2. How to find the lowest common multiple of 102 and 107?

To find the lowest common multiple of 102 and 107, we have to get the multip;es of both numbers and identify the least common multiple in them which is 10914.

3. What are the Factors of 102?

Answer: Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. There are 8 integers that are factors of 102. The greatest factor of 102 is 102.

4. What are the Factors of 107?

Answer: Factors of 107 are 1, 107. There are 2 integers that are factors of 107. The greatest factor of 107 is 107.

Answer:

Least Common Multiple of 102 and 107 = 10914

Step 1: Find the prime factorization of 102

102 = 2 x 3 x 17

Step 2: Find the prime factorization of 107

107 = 107

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

LCM = 10914 = 2 x 3 x 17 x 107

Step 4: Therefore, the least common multiple of 102 and 107 is 10914.