Given Numbers are 6965, 6972

We can find the LCM of 6965, 6972 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 6965 and 6972

Multiples of 6965 =6965,13930,20895,27860,34825,41790,48755,55720,62685,69650,76615,83580,90545,97510,104475,111440,118405,

Multiples of 6972 =6972,13944,20916,27888,34860,41832,48804,55776,62748,69720,76692,83664,90636,97608,104580,111552,118524,

Now, get the least common multiple of 6965, 6972 which is 6937140

So, the LCM of 6965, 6972 is 6937140.

One method for determining the LCM of 6965 and 6972 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 6965's prime factorization:

Prime factors of 6965 are 5, 7,199.

6965 = 5¹×7¹×199¹

And this is 6972's prime factorization:

Prime factors of 6972 are 2, 3, 7,83.

6972 = 2²×3¹×7¹×83¹

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: 5, 7,199, 2, 3,83

2²×3¹×5¹×7¹×83¹×199¹ = 6937140

This shows that the LCM of 6965 and 6972 is 6937140.

The first step in determining the Least Common Multiple of 6965 and 6972 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 6965 and 6972:

Lets look at the first ten multiples of these numbers, 6965 and 6972:

6965,13930,20895,27860,34825,41790,48755,55720,62685,118405 are the first ten multiples of 6965.

6972,13944,20916,27888,34860,41832,48804,55776,62748,118524 are the first ten multiples of 6972.

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 6965 and 6972, for example, are 83580, 118405, and 111552. 6937140 is the least common multiple since it is the smallest.

6965 and 6972 have an LCM of 6937140.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6965 and 6972, than apply into the LCM equation.

GCF(6965,6972) = 7
LCM(6965,6972) = ( 6965 × 6972) / 7
LCM(6965,6972) = 48559980 / 7
LCM(6965,6972) = 6937140

1. What is the LCM of 6965 and 6972?

The LCM of 6965 and 6972 is 6937140.

2. How to find the lowest common multiple of 6965 and 6972?

To find the lowest common multiple of 6965 and 6972, we have to get the multip;es of both numbers and identify the least common multiple in them which is 6937140.

3. What are the Factors of 6965?

Answer: Factors of 6965 are 1, 5, 7, 35, 199, 995, 1393, 6965. There are 8 integers that are factors of 6965. The greatest factor of 6965 is 6965.

4. What are the Factors of 6972?

Answer: Factors of 6972 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 83, 84, 166, 249, 332, 498, 581, 996, 1162, 1743, 2324, 3486, 6972. There are 24 integers that are factors of 6972. The greatest factor of 6972 is 6972.

Answer:

Least Common Multiple of 6965 and 6972 = 6937140

Step 1: Find the prime factorization of 6965

6965 = 5 x 7 x 199

Step 2: Find the prime factorization of 6972

6972 = 2 x 2 x 3 x 7 x 83

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

LCM = 6937140 = 2 x 2 x 3 x 5 x 7 x 83 x 199

Step 4: Therefore, the least common multiple of 6965 and 6972 is 6937140.