Given Numbers are 7031, 7038

We can find the LCM of 7031, 7038 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 7031 and 7038

Multiples of 7031 =7031,14062,21093,28124,35155,42186,49217,56248,63279,70310,77341,84372,91403,98434,105465,112496,119527,

Multiples of 7038 =7038,14076,21114,28152,35190,42228,49266,56304,63342,70380,77418,84456,91494,98532,105570,112608,119646,

Now, get the least common multiple of 7031, 7038 which is 49484178

So, the LCM of 7031, 7038 is 49484178.

One method for determining the LCM of 7031 and 7038 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 7031's prime factorization:

Prime factors of 7031 are 79,89.

7031 = 79¹×89¹

And this is 7038's prime factorization:

Prime factors of 7038 are 2, 3, 17,23.

7038 = 2¹×3²×17¹×23¹

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: 79,89, 2, 3, 17,23

2¹×3²×17¹×23¹×79¹×89¹ = 49484178

This shows that the LCM of 7031 and 7038 is 49484178.

The first step in determining the Least Common Multiple of 7031 and 7038 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 7031 and 7038:

Lets look at the first ten multiples of these numbers, 7031 and 7038:

7031,14062,21093,28124,35155,42186,49217,56248,63279,119527 are the first ten multiples of 7031.

7038,14076,21114,28152,35190,42228,49266,56304,63342,119646 are the first ten multiples of 7038.

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 7031 and 7038, for example, are 84372, 119527, and 112608. 49484178 is the least common multiple since it is the smallest.

7031 and 7038 have an LCM of 49484178.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7031 and 7038, than apply into the LCM equation.

GCF(7031,7038) = 1
LCM(7031,7038) = ( 7031 × 7038) / 1
LCM(7031,7038) = 49484178 / 1
LCM(7031,7038) = 49484178

1. What is the LCM of 7031 and 7038?

The LCM of 7031 and 7038 is 49484178.

2. How to find the lowest common multiple of 7031 and 7038?

To find the lowest common multiple of 7031 and 7038, we have to get the multip;es of both numbers and identify the least common multiple in them which is 49484178.

3. What are the Factors of 7031?

Answer: Factors of 7031 are 1, 79, 89, 7031. There are 4 integers that are factors of 7031. The greatest factor of 7031 is 7031.

4. What are the Factors of 7038?

Answer: Factors of 7038 are 1, 2, 3, 6, 9, 17, 18, 23, 34, 46, 51, 69, 102, 138, 153, 207, 306, 391, 414, 782, 1173, 2346, 3519, 7038. There are 24 integers that are factors of 7038. The greatest factor of 7038 is 7038.

Answer:

Least Common Multiple of 7031 and 7038 = 49484178

Step 1: Find the prime factorization of 7031

7031 = 79 x 89

Step 2: Find the prime factorization of 7038

7038 = 2 x 3 x 3 x 17 x 23

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

LCM = 49484178 = 2 x 3 x 3 x 17 x 23 x 79 x 89

Step 4: Therefore, the least common multiple of 7031 and 7038 is 49484178.