Given Numbers are 107, 114

We can find the LCM of 107, 114 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 107 and 114

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

Multiples of 114 =114,228,342,456,570,684,798,912,1026,1140,1254,1368,1482,1596,1710,1824,1938,

Now, get the least common multiple of 107, 114 which is 12198

So, the LCM of 107, 114 is 12198.

One method for determining the LCM of 107 and 114 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 107's prime factorization:

Prime factors of 107 are 107.

107 = 107¹

And this is 114's prime factorization:

Prime factors of 114 are 2, 3,19.

114 = 2¹×3¹×19¹

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:107, 2, 3,19

2¹×3¹×19¹×107¹ = 12198

This shows that the LCM of 107 and 114 is 12198.

The first step in determining the Least Common Multiple of 107 and 114 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 107 and 114:

Lets look at the first ten multiples of these numbers, 107 and 114:

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

114,228,342,456,570,684,798,912,1026,1938 are the first ten multiples of 114.

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 107 and 114, for example, are 1284, 1819, and 1824. 12198 is the least common multiple since it is the smallest.

107 and 114 have an LCM of 12198.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 107 and 114, than apply into the LCM equation.

GCF(107,114) = 1
LCM(107,114) = ( 107 × 114) / 1
LCM(107,114) = 12198 / 1
LCM(107,114) = 12198

1. What is the LCM of 107 and 114?

The LCM of 107 and 114 is 12198.

2. How to find the lowest common multiple of 107 and 114?

To find the lowest common multiple of 107 and 114, we have to get the multip;es of both numbers and identify the least common multiple in them which is 12198.

3. 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.

4. What are the Factors of 114?

Answer: Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. There are 8 integers that are factors of 114. The greatest factor of 114 is 114.

Answer:

Least Common Multiple of 107 and 114 = 12198

Step 1: Find the prime factorization of 107

107 = 107

Step 2: Find the prime factorization of 114

114 = 2 x 3 x 19

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

LCM = 12198 = 2 x 3 x 19 x 107

Step 4: Therefore, the least common multiple of 107 and 114 is 12198.