Given Numbers are 972, 980

We can find the LCM of 972, 980 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 972 and 980

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

Multiples of 980 =980,1960,2940,3920,4900,5880,6860,7840,8820,9800,10780,11760,12740,13720,14700,15680,16660,

Now, get the least common multiple of 972, 980 which is 238140

So, the LCM of 972, 980 is 238140.

One method for determining the LCM of 972 and 980 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 980's prime factorization:

Prime factors of 980 are 2, 5,7.

980 = 2²×5¹×7²

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, 5,7

2²×3⁵×5¹×7² = 238140

This shows that the LCM of 972 and 980 is 238140.

The first step in determining the Least Common Multiple of 972 and 980 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 972 and 980:

Lets look at the first ten multiples of these numbers, 972 and 980:

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

980,1960,2940,3920,4900,5880,6860,7840,8820,16660 are the first ten multiples of 980.

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 980, for example, are 11664, 16524, and 15680. 238140 is the least common multiple since it is the smallest.

972 and 980 have an LCM of 238140.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 972 and 980, than apply into the LCM equation.

GCF(972,980) = 4
LCM(972,980) = ( 972 × 980) / 4
LCM(972,980) = 952560 / 4
LCM(972,980) = 238140

1. What is the LCM of 972 and 980?

The LCM of 972 and 980 is 238140.

2. How to find the lowest common multiple of 972 and 980?

To find the lowest common multiple of 972 and 980, we have to get the multip;es of both numbers and identify the least common multiple in them which is 238140.

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 980?

Answer: Factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980. There are 18 integers that are factors of 980. The greatest factor of 980 is 980.

Answer:

Least Common Multiple of 972 and 980 = 238140

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 980

980 = 2 x 2 x 5 x 7 x 7

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

LCM = 238140 = 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5 x 7 x 7

Step 4: Therefore, the least common multiple of 972 and 980 is 238140.