Given Numbers are 97, 103

We can find the LCM of 97, 103 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 97 and 103

Multiples of 97 =97,194,291,388,485,582,679,776,873,970,1067,1164,1261,1358,1455,1552,1649,

Multiples of 103 =103,206,309,412,515,618,721,824,927,1030,1133,1236,1339,1442,1545,1648,1751,

Now, get the least common multiple of 97, 103 which is 9991

So, the LCM of 97, 103 is 9991.

One method for determining the LCM of 97 and 103 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 97's prime factorization:

Prime factors of 97 are 97.

97 = 97¹

And this is 103's prime factorization:

Prime factors of 103 are 103.

103 = 103¹

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:97,103

97¹×103¹ = 9991

This shows that the LCM of 97 and 103 is 9991.

The first step in determining the Least Common Multiple of 97 and 103 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 97 and 103:

Lets look at the first ten multiples of these numbers, 97 and 103:

97,194,291,388,485,582,679,776,873,1649 are the first ten multiples of 97.

103,206,309,412,515,618,721,824,927,1751 are the first ten multiples of 103.

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 97 and 103, for example, are 1164, 1649, and 1648. 9991 is the least common multiple since it is the smallest.

97 and 103 have an LCM of 9991.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 97 and 103, than apply into the LCM equation.

GCF(97,103) = 1
LCM(97,103) = ( 97 × 103) / 1
LCM(97,103) = 9991 / 1
LCM(97,103) = 9991

1. What is the LCM of 97 and 103?

The LCM of 97 and 103 is 9991.

2. How to find the lowest common multiple of 97 and 103?

To find the lowest common multiple of 97 and 103, we have to get the multip;es of both numbers and identify the least common multiple in them which is 9991.

3. What are the Factors of 97?

Answer: Factors of 97 are 1, 97. There are 2 integers that are factors of 97. The greatest factor of 97 is 97.

4. What are the Factors of 103?

Answer: Factors of 103 are 1, 103. There are 2 integers that are factors of 103. The greatest factor of 103 is 103.

Answer:

Least Common Multiple of 97 and 103 = 9991

Step 1: Find the prime factorization of 97

97 = 97

Step 2: Find the prime factorization of 103

103 = 103

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

LCM = 9991 = 97 x 103

Step 4: Therefore, the least common multiple of 97 and 103 is 9991.