Given Numbers are 207, 214

We can find the LCM of 207, 214 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 207 and 214

Multiples of 207 =207,414,621,828,1035,1242,1449,1656,1863,2070,2277,2484,2691,2898,3105,3312,3519,

Multiples of 214 =214,428,642,856,1070,1284,1498,1712,1926,2140,2354,2568,2782,2996,3210,3424,3638,

Now, get the least common multiple of 207, 214 which is 44298

So, the LCM of 207, 214 is 44298.

One method for determining the LCM of 207 and 214 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 207's prime factorization:

Prime factors of 207 are 3,23.

207 = 3²×23¹

And this is 214's prime factorization:

Prime factors of 214 are 2,107.

214 = 2¹×107¹

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: 3,23, 2,107

2¹×3²×23¹×107¹ = 44298

This shows that the LCM of 207 and 214 is 44298.

The first step in determining the Least Common Multiple of 207 and 214 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 207 and 214:

Lets look at the first ten multiples of these numbers, 207 and 214:

207,414,621,828,1035,1242,1449,1656,1863,3519 are the first ten multiples of 207.

214,428,642,856,1070,1284,1498,1712,1926,3638 are the first ten multiples of 214.

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 207 and 214, for example, are 2484, 3519, and 3424. 44298 is the least common multiple since it is the smallest.

207 and 214 have an LCM of 44298.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 207 and 214, than apply into the LCM equation.

GCF(207,214) = 1
LCM(207,214) = ( 207 × 214) / 1
LCM(207,214) = 44298 / 1
LCM(207,214) = 44298

1. What is the LCM of 207 and 214?

The LCM of 207 and 214 is 44298.

2. How to find the lowest common multiple of 207 and 214?

To find the lowest common multiple of 207 and 214, we have to get the multip;es of both numbers and identify the least common multiple in them which is 44298.

3. What are the Factors of 207?

Answer: Factors of 207 are 1, 3, 9, 23, 69, 207. There are 6 integers that are factors of 207. The greatest factor of 207 is 207.

4. What are the Factors of 214?

Answer: Factors of 214 are 1, 2, 107, 214. There are 4 integers that are factors of 214. The greatest factor of 214 is 214.

Answer:

Least Common Multiple of 207 and 214 = 44298

Step 1: Find the prime factorization of 207

207 = 3 x 3 x 23

Step 2: Find the prime factorization of 214

214 = 2 x 107

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

LCM = 44298 = 2 x 3 x 3 x 23 x 107

Step 4: Therefore, the least common multiple of 207 and 214 is 44298.