Given Numbers are 23, 31

We can find the LCM of 23, 31 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 23 and 31

Multiples of 23 =23,46,69,92,115,138,161,184,207,230,253,276,299,322,345,368,391,

Multiples of 31 =31,62,93,124,155,186,217,248,279,310,341,372,403,434,465,496,527,

Now, get the least common multiple of 23, 31 which is 713

So, the LCM of 23, 31 is 713.

One method for determining the LCM of 23 and 31 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 23's prime factorization:

Prime factors of 23 are 23.

23 = 23¹

And this is 31's prime factorization:

Prime factors of 31 are 31.

31 = 31¹

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:23,31

23¹×31¹ = 713

This shows that the LCM of 23 and 31 is 713.

The first step in determining the Least Common Multiple of 23 and 31 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 23 and 31:

Lets look at the first ten multiples of these numbers, 23 and 31:

23,46,69,92,115,138,161,184,207,391 are the first ten multiples of 23.

31,62,93,124,155,186,217,248,279,527 are the first ten multiples of 31.

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 23 and 31, for example, are 276, 391, and 496. 713 is the least common multiple since it is the smallest.

23 and 31 have an LCM of 713.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 23 and 31, than apply into the LCM equation.

GCF(23,31) = 1
LCM(23,31) = ( 23 × 31) / 1
LCM(23,31) = 713 / 1
LCM(23,31) = 713

1. What is the LCM of 23 and 31?

The LCM of 23 and 31 is 713.

2. How to find the lowest common multiple of 23 and 31?

To find the lowest common multiple of 23 and 31, we have to get the multip;es of both numbers and identify the least common multiple in them which is 713.

3. What are the Factors of 23?

Answer: Factors of 23 are 1, 23. There are 2 integers that are factors of 23. The greatest factor of 23 is 23.

4. What are the Factors of 31?

Answer: Factors of 31 are 1, 31. There are 2 integers that are factors of 31. The greatest factor of 31 is 31.

Answer:

Least Common Multiple of 23 and 31 = 713

Step 1: Find the prime factorization of 23

23 = 23

Step 2: Find the prime factorization of 31

31 = 31

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

LCM = 713 = 23 x 31

Step 4: Therefore, the least common multiple of 23 and 31 is 713.