Given Numbers are 972, 976

We can find the LCM of 972, 976 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 972 and 976

Multiples of 972 =972,1944,2916,3888,4860,5832,6804,7776,8748,9720,10692,11664,12636,13608,14580,15552,16524,

Multiples of 976 =976,1952,2928,3904,4880,5856,6832,7808,8784,9760,10736,11712,12688,13664,14640,15616,16592,

Now, get the least common multiple of 972, 976 which is 237168

So, the LCM of 972, 976 is 237168.

One method for determining the LCM of 972 and 976 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 972's prime factorization:

Prime factors of 972 are 2,3.

972 = 2²×3⁵

And this is 976's prime factorization:

Prime factors of 976 are 2,61.

976 = 2⁴×61¹

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: 2,3,61

2⁴×3⁵×61¹ = 237168

This shows that the LCM of 972 and 976 is 237168.

The first step in determining the Least Common Multiple of 972 and 976 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 972 and 976:

Lets look at the first ten multiples of these numbers, 972 and 976:

972,1944,2916,3888,4860,5832,6804,7776,8748,16524 are the first ten multiples of 972.

976,1952,2928,3904,4880,5856,6832,7808,8784,16592 are the first ten multiples of 976.

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 972 and 976, for example, are 11664, 16524, and 15616. 237168 is the least common multiple since it is the smallest.

972 and 976 have an LCM of 237168.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 972 and 976, than apply into the LCM equation.

GCF(972,976) = 4
LCM(972,976) = ( 972 × 976) / 4
LCM(972,976) = 948672 / 4
LCM(972,976) = 237168

1. What is the LCM of 972 and 976?

The LCM of 972 and 976 is 237168.

2. How to find the lowest common multiple of 972 and 976?

To find the lowest common multiple of 972 and 976, we have to get the multip;es of both numbers and identify the least common multiple in them which is 237168.

3. What are the Factors of 972?

Answer: Factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972. There are 18 integers that are factors of 972. The greatest factor of 972 is 972.

4. What are the Factors of 976?

Answer: Factors of 976 are 1, 2, 4, 8, 16, 61, 122, 244, 488, 976. There are 10 integers that are factors of 976. The greatest factor of 976 is 976.

Answer:

Least Common Multiple of 972 and 976 = 237168

Step 1: Find the prime factorization of 972

972 = 2 x 2 x 3 x 3 x 3 x 3 x 3

Step 2: Find the prime factorization of 976

976 = 2 x 2 x 2 x 2 x 61

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

LCM = 237168 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 61

Step 4: Therefore, the least common multiple of 972 and 976 is 237168.