Given Numbers are 6975, 6980

We can find the LCM of 6975, 6980 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 6975 and 6980

Multiples of 6975 =6975,13950,20925,27900,34875,41850,48825,55800,62775,69750,76725,83700,90675,97650,104625,111600,118575,

Multiples of 6980 =6980,13960,20940,27920,34900,41880,48860,55840,62820,69800,76780,83760,90740,97720,104700,111680,118660,

Now, get the least common multiple of 6975, 6980 which is 9737100

So, the LCM of 6975, 6980 is 9737100.

One method for determining the LCM of 6975 and 6980 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 6975's prime factorization:

Prime factors of 6975 are 3, 5,31.

6975 = 3²×5²×31¹

And this is 6980's prime factorization:

Prime factors of 6980 are 2, 5,349.

6980 = 2²×5¹×349¹

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, 5,31, 2,349

2²×3²×5²×31¹×349¹ = 9737100

This shows that the LCM of 6975 and 6980 is 9737100.

The first step in determining the Least Common Multiple of 6975 and 6980 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 6975 and 6980:

Lets look at the first ten multiples of these numbers, 6975 and 6980:

6975,13950,20925,27900,34875,41850,48825,55800,62775,118575 are the first ten multiples of 6975.

6980,13960,20940,27920,34900,41880,48860,55840,62820,118660 are the first ten multiples of 6980.

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 6975 and 6980, for example, are 83700, 118575, and 111680. 9737100 is the least common multiple since it is the smallest.

6975 and 6980 have an LCM of 9737100.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6975 and 6980, than apply into the LCM equation.

GCF(6975,6980) = 5
LCM(6975,6980) = ( 6975 × 6980) / 5
LCM(6975,6980) = 48685500 / 5
LCM(6975,6980) = 9737100

1. What is the LCM of 6975 and 6980?

The LCM of 6975 and 6980 is 9737100.

2. How to find the lowest common multiple of 6975 and 6980?

To find the lowest common multiple of 6975 and 6980, we have to get the multip;es of both numbers and identify the least common multiple in them which is 9737100.

3. What are the Factors of 6975?

Answer: Factors of 6975 are 1, 3, 5, 9, 15, 25, 31, 45, 75, 93, 155, 225, 279, 465, 775, 1395, 2325, 6975. There are 18 integers that are factors of 6975. The greatest factor of 6975 is 6975.

4. What are the Factors of 6980?

Answer: Factors of 6980 are 1, 2, 4, 5, 10, 20, 349, 698, 1396, 1745, 3490, 6980. There are 12 integers that are factors of 6980. The greatest factor of 6980 is 6980.

Answer:

Least Common Multiple of 6975 and 6980 = 9737100

Step 1: Find the prime factorization of 6975

6975 = 3 x 3 x 5 x 5 x 31

Step 2: Find the prime factorization of 6980

6980 = 2 x 2 x 5 x 349

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

LCM = 9737100 = 2 x 2 x 3 x 3 x 5 x 5 x 31 x 349

Step 4: Therefore, the least common multiple of 6975 and 6980 is 9737100.