Given Numbers are 7005, 7012

We can find the LCM of 7005, 7012 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 7005 and 7012

Multiples of 7005 =7005,14010,21015,28020,35025,42030,49035,56040,63045,70050,77055,84060,91065,98070,105075,112080,119085,

Multiples of 7012 =7012,14024,21036,28048,35060,42072,49084,56096,63108,70120,77132,84144,91156,98168,105180,112192,119204,

Now, get the least common multiple of 7005, 7012 which is 49119060

So, the LCM of 7005, 7012 is 49119060.

One method for determining the LCM of 7005 and 7012 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 7005's prime factorization:

Prime factors of 7005 are 3, 5,467.

7005 = 3¹×5¹×467¹

And this is 7012's prime factorization:

Prime factors of 7012 are 2,1753.

7012 = 2²×1753¹

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: 3, 5,467, 2,1753

2²×3¹×5¹×467¹×1753¹ = 49119060

This shows that the LCM of 7005 and 7012 is 49119060.

The first step in determining the Least Common Multiple of 7005 and 7012 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 7005 and 7012:

Lets look at the first ten multiples of these numbers, 7005 and 7012:

7005,14010,21015,28020,35025,42030,49035,56040,63045,119085 are the first ten multiples of 7005.

7012,14024,21036,28048,35060,42072,49084,56096,63108,119204 are the first ten multiples of 7012.

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 7005 and 7012, for example, are 84060, 119085, and 112192. 49119060 is the least common multiple since it is the smallest.

7005 and 7012 have an LCM of 49119060.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7005 and 7012, than apply into the LCM equation.

GCF(7005,7012) = 1
LCM(7005,7012) = ( 7005 × 7012) / 1
LCM(7005,7012) = 49119060 / 1
LCM(7005,7012) = 49119060

1. What is the LCM of 7005 and 7012?

The LCM of 7005 and 7012 is 49119060.

2. How to find the lowest common multiple of 7005 and 7012?

To find the lowest common multiple of 7005 and 7012, we have to get the multip;es of both numbers and identify the least common multiple in them which is 49119060.

3. What are the Factors of 7005?

Answer: Factors of 7005 are 1, 3, 5, 15, 467, 1401, 2335, 7005. There are 8 integers that are factors of 7005. The greatest factor of 7005 is 7005.

4. What are the Factors of 7012?

Answer: Factors of 7012 are 1, 2, 4, 1753, 3506, 7012. There are 6 integers that are factors of 7012. The greatest factor of 7012 is 7012.

Answer:

Least Common Multiple of 7005 and 7012 = 49119060

Step 1: Find the prime factorization of 7005

7005 = 3 x 5 x 467

Step 2: Find the prime factorization of 7012

7012 = 2 x 2 x 1753

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

LCM = 49119060 = 2 x 2 x 3 x 5 x 467 x 1753

Step 4: Therefore, the least common multiple of 7005 and 7012 is 49119060.