Given Numbers are 7003, 7008

We can find the LCM of 7003, 7008 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 7003 and 7008

Multiples of 7003 =7003,14006,21009,28012,35015,42018,49021,56024,63027,70030,77033,84036,91039,98042,105045,112048,119051,

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

Now, get the least common multiple of 7003, 7008 which is 49077024

So, the LCM of 7003, 7008 is 49077024.

One method for determining the LCM of 7003 and 7008 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 7003's prime factorization:

Prime factors of 7003 are 47,149.

7003 = 47¹×149¹

And this is 7008's prime factorization:

Prime factors of 7008 are 2, 3,73.

7008 = 2⁵×3¹×73¹

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: 47,149, 2, 3,73

2⁵×3¹×47¹×73¹×149¹ = 49077024

This shows that the LCM of 7003 and 7008 is 49077024.

The first step in determining the Least Common Multiple of 7003 and 7008 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 7003 and 7008:

Lets look at the first ten multiples of these numbers, 7003 and 7008:

7003,14006,21009,28012,35015,42018,49021,56024,63027,119051 are the first ten multiples of 7003.

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

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 7003 and 7008, for example, are 84036, 119051, and 112128. 49077024 is the least common multiple since it is the smallest.

7003 and 7008 have an LCM of 49077024.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7003 and 7008, than apply into the LCM equation.

GCF(7003,7008) = 1
LCM(7003,7008) = ( 7003 × 7008) / 1
LCM(7003,7008) = 49077024 / 1
LCM(7003,7008) = 49077024

1. What is the LCM of 7003 and 7008?

The LCM of 7003 and 7008 is 49077024.

2. How to find the lowest common multiple of 7003 and 7008?

To find the lowest common multiple of 7003 and 7008, we have to get the multip;es of both numbers and identify the least common multiple in them which is 49077024.

3. What are the Factors of 7003?

Answer: Factors of 7003 are 1, 47, 149, 7003. There are 4 integers that are factors of 7003. The greatest factor of 7003 is 7003.

4. 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.

Answer:

Least Common Multiple of 7003 and 7008 = 49077024

Step 1: Find the prime factorization of 7003

7003 = 47 x 149

Step 2: Find the prime factorization of 7008

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

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

LCM = 49077024 = 2 x 2 x 2 x 2 x 2 x 3 x 47 x 73 x 149

Step 4: Therefore, the least common multiple of 7003 and 7008 is 49077024.