Given Numbers are 7009, 7014

We can find the LCM of 7009, 7014 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 7009 and 7014

Multiples of 7009 =7009,14018,21027,28036,35045,42054,49063,56072,63081,70090,77099,84108,91117,98126,105135,112144,119153,

Multiples of 7014 =7014,14028,21042,28056,35070,42084,49098,56112,63126,70140,77154,84168,91182,98196,105210,112224,119238,

Now, get the least common multiple of 7009, 7014 which is 49161126

So, the LCM of 7009, 7014 is 49161126.

One method for determining the LCM of 7009 and 7014 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 7009's prime factorization:

Prime factors of 7009 are 43,163.

7009 = 43¹×163¹

And this is 7014's prime factorization:

Prime factors of 7014 are 2, 3, 7,167.

7014 = 2¹×3¹×7¹×167¹

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: 43,163, 2, 3, 7,167

2¹×3¹×7¹×43¹×163¹×167¹ = 49161126

This shows that the LCM of 7009 and 7014 is 49161126.

The first step in determining the Least Common Multiple of 7009 and 7014 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 7009 and 7014:

Lets look at the first ten multiples of these numbers, 7009 and 7014:

7009,14018,21027,28036,35045,42054,49063,56072,63081,119153 are the first ten multiples of 7009.

7014,14028,21042,28056,35070,42084,49098,56112,63126,119238 are the first ten multiples of 7014.

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 7009 and 7014, for example, are 84108, 119153, and 112224. 49161126 is the least common multiple since it is the smallest.

7009 and 7014 have an LCM of 49161126.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7009 and 7014, than apply into the LCM equation.

GCF(7009,7014) = 1
LCM(7009,7014) = ( 7009 × 7014) / 1
LCM(7009,7014) = 49161126 / 1
LCM(7009,7014) = 49161126

1. What is the LCM of 7009 and 7014?

The LCM of 7009 and 7014 is 49161126.

2. How to find the lowest common multiple of 7009 and 7014?

To find the lowest common multiple of 7009 and 7014, we have to get the multip;es of both numbers and identify the least common multiple in them which is 49161126.

3. What are the Factors of 7009?

Answer: Factors of 7009 are 1, 43, 163, 7009. There are 4 integers that are factors of 7009. The greatest factor of 7009 is 7009.

4. What are the Factors of 7014?

Answer: Factors of 7014 are 1, 2, 3, 6, 7, 14, 21, 42, 167, 334, 501, 1002, 1169, 2338, 3507, 7014. There are 16 integers that are factors of 7014. The greatest factor of 7014 is 7014.

Answer:

Least Common Multiple of 7009 and 7014 = 49161126

Step 1: Find the prime factorization of 7009

7009 = 43 x 163

Step 2: Find the prime factorization of 7014

7014 = 2 x 3 x 7 x 167

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

LCM = 49161126 = 2 x 3 x 7 x 43 x 163 x 167

Step 4: Therefore, the least common multiple of 7009 and 7014 is 49161126.