Given Numbers are 6978, 6984

We can find the LCM of 6978, 6984 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 6978 and 6984

Multiples of 6978 =6978,13956,20934,27912,34890,41868,48846,55824,62802,69780,76758,83736,90714,97692,104670,111648,118626,

Multiples of 6984 =6984,13968,20952,27936,34920,41904,48888,55872,62856,69840,76824,83808,90792,97776,104760,111744,118728,

Now, get the least common multiple of 6978, 6984 which is 8122392

So, the LCM of 6978, 6984 is 8122392.

One method for determining the LCM of 6978 and 6984 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 6978's prime factorization:

Prime factors of 6978 are 2, 3,1163.

6978 = 2¹×3¹×1163¹

And this is 6984's prime factorization:

Prime factors of 6984 are 2, 3,97.

6984 = 2³×3²×97¹

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, 3,1163,97

2³×3²×97¹×1163¹ = 8122392

This shows that the LCM of 6978 and 6984 is 8122392.

The first step in determining the Least Common Multiple of 6978 and 6984 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 6978 and 6984:

Lets look at the first ten multiples of these numbers, 6978 and 6984:

6978,13956,20934,27912,34890,41868,48846,55824,62802,118626 are the first ten multiples of 6978.

6984,13968,20952,27936,34920,41904,48888,55872,62856,118728 are the first ten multiples of 6984.

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 6978 and 6984, for example, are 83736, 118626, and 111744. 8122392 is the least common multiple since it is the smallest.

6978 and 6984 have an LCM of 8122392.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6978 and 6984, than apply into the LCM equation.

GCF(6978,6984) = 6
LCM(6978,6984) = ( 6978 × 6984) / 6
LCM(6978,6984) = 48734352 / 6
LCM(6978,6984) = 8122392

1. What is the LCM of 6978 and 6984?

The LCM of 6978 and 6984 is 8122392.

2. How to find the lowest common multiple of 6978 and 6984?

To find the lowest common multiple of 6978 and 6984, we have to get the multip;es of both numbers and identify the least common multiple in them which is 8122392.

3. What are the Factors of 6978?

Answer: Factors of 6978 are 1, 2, 3, 6, 1163, 2326, 3489, 6978. There are 8 integers that are factors of 6978. The greatest factor of 6978 is 6978.

4. What are the Factors of 6984?

Answer: Factors of 6984 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 97, 194, 291, 388, 582, 776, 873, 1164, 1746, 2328, 3492, 6984. There are 24 integers that are factors of 6984. The greatest factor of 6984 is 6984.

Answer:

Least Common Multiple of 6978 and 6984 = 8122392

Step 1: Find the prime factorization of 6978

6978 = 2 x 3 x 1163

Step 2: Find the prime factorization of 6984

6984 = 2 x 2 x 2 x 3 x 3 x 97

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

LCM = 8122392 = 2 x 2 x 2 x 3 x 3 x 97 x 1163

Step 4: Therefore, the least common multiple of 6978 and 6984 is 8122392.