Given Numbers are 7002, 7006

We can find the LCM of 7002, 7006 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 7002 and 7006

Multiples of 7002 =7002,14004,21006,28008,35010,42012,49014,56016,63018,70020,77022,84024,91026,98028,105030,112032,119034,

Multiples of 7006 =7006,14012,21018,28024,35030,42036,49042,56048,63054,70060,77066,84072,91078,98084,105090,112096,119102,

Now, get the least common multiple of 7002, 7006 which is 24528006

So, the LCM of 7002, 7006 is 24528006.

One method for determining the LCM of 7002 and 7006 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 7002's prime factorization:

Prime factors of 7002 are 2, 3,389.

7002 = 2¹×3²×389¹

And this is 7006's prime factorization:

Prime factors of 7006 are 2, 31,113.

7006 = 2¹×31¹×113¹

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, 3,389, 31,113

2¹×3²×31¹×113¹×389¹ = 24528006

This shows that the LCM of 7002 and 7006 is 24528006.

The first step in determining the Least Common Multiple of 7002 and 7006 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 7002 and 7006:

Lets look at the first ten multiples of these numbers, 7002 and 7006:

7002,14004,21006,28008,35010,42012,49014,56016,63018,119034 are the first ten multiples of 7002.

7006,14012,21018,28024,35030,42036,49042,56048,63054,119102 are the first ten multiples of 7006.

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 7002 and 7006, for example, are 84024, 119034, and 112096. 24528006 is the least common multiple since it is the smallest.

7002 and 7006 have an LCM of 24528006.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7002 and 7006, than apply into the LCM equation.

GCF(7002,7006) = 2
LCM(7002,7006) = ( 7002 × 7006) / 2
LCM(7002,7006) = 49056012 / 2
LCM(7002,7006) = 24528006

1. What is the LCM of 7002 and 7006?

The LCM of 7002 and 7006 is 24528006.

2. How to find the lowest common multiple of 7002 and 7006?

To find the lowest common multiple of 7002 and 7006, we have to get the multip;es of both numbers and identify the least common multiple in them which is 24528006.

3. What are the Factors of 7002?

Answer: Factors of 7002 are 1, 2, 3, 6, 9, 18, 389, 778, 1167, 2334, 3501, 7002. There are 12 integers that are factors of 7002. The greatest factor of 7002 is 7002.

4. What are the Factors of 7006?

Answer: Factors of 7006 are 1, 2, 31, 62, 113, 226, 3503, 7006. There are 8 integers that are factors of 7006. The greatest factor of 7006 is 7006.

Answer:

Least Common Multiple of 7002 and 7006 = 24528006

Step 1: Find the prime factorization of 7002

7002 = 2 x 3 x 3 x 389

Step 2: Find the prime factorization of 7006

7006 = 2 x 31 x 113

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

LCM = 24528006 = 2 x 3 x 3 x 31 x 113 x 389

Step 4: Therefore, the least common multiple of 7002 and 7006 is 24528006.