Given Numbers are 7008, 7014

We can find the LCM of 7008, 7014 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 7008 and 7014

Multiples of 7008 =7008,14016,21024,28032,35040,42048,49056,56064,63072,70080,77088,84096,91104,98112,105120,112128,119136,

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 7008, 7014 which is 8192352

So, the LCM of 7008, 7014 is 8192352.

One method for determining the LCM of 7008 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 7008's prime factorization:

Prime factors of 7008 are 2, 3,73.

7008 = 2⁵×3¹×73¹

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: 2, 3,73, 7,167

2⁵×3¹×7¹×73¹×167¹ = 8192352

This shows that the LCM of 7008 and 7014 is 8192352.

The first step in determining the Least Common Multiple of 7008 and 7014 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 7008 and 7014:

Lets look at the first ten multiples of these numbers, 7008 and 7014:

7008,14016,21024,28032,35040,42048,49056,56064,63072,119136 are the first ten multiples of 7008.

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 7008 and 7014, for example, are 84096, 119136, and 112224. 8192352 is the least common multiple since it is the smallest.

7008 and 7014 have an LCM of 8192352.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7008 and 7014, than apply into the LCM equation.

GCF(7008,7014) = 6
LCM(7008,7014) = ( 7008 × 7014) / 6
LCM(7008,7014) = 49154112 / 6
LCM(7008,7014) = 8192352

1. What is the LCM of 7008 and 7014?

The LCM of 7008 and 7014 is 8192352.

2. How to find the lowest common multiple of 7008 and 7014?

To find the lowest common multiple of 7008 and 7014, we have to get the multip;es of both numbers and identify the least common multiple in them which is 8192352.

3. What are the Factors of 7008?

Answer: Factors of 7008 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 73, 96, 146, 219, 292, 438, 584, 876, 1168, 1752, 2336, 3504, 7008. There are 24 integers that are factors of 7008. The greatest factor of 7008 is 7008.

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 7008 and 7014 = 8192352

Step 1: Find the prime factorization of 7008

7008 = 2 x 2 x 2 x 2 x 2 x 3 x 73

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 = 8192352 = 2 x 2 x 2 x 2 x 2 x 3 x 7 x 73 x 167

Step 4: Therefore, the least common multiple of 7008 and 7014 is 8192352.