Given Numbers are 13, 21

We can find the LCM of 13, 21 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 13 and 21

Multiples of 13 =13,26,39,52,65,78,91,104,117,130,143,156,169,182,195,208,221,

Multiples of 21 =21,42,63,84,105,126,147,168,189,210,231,252,273,294,315,336,357,

Now, get the least common multiple of 13, 21 which is 273

So, the LCM of 13, 21 is 273.

One method for determining the LCM of 13 and 21 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 13's prime factorization:

Prime factors of 13 are 13.

13 = 13¹

And this is 21's prime factorization:

Prime factors of 21 are 3,7.

21 = 3¹×7¹

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:13, 3,7

3¹×7¹×13¹ = 273

This shows that the LCM of 13 and 21 is 273.

The first step in determining the Least Common Multiple of 13 and 21 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 13 and 21:

Lets look at the first ten multiples of these numbers, 13 and 21:

13,26,39,52,65,78,91,104,117,221 are the first ten multiples of 13.

21,42,63,84,105,126,147,168,189,357 are the first ten multiples of 21.

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 13 and 21, for example, are 156, 221, and 336. 273 is the least common multiple since it is the smallest.

13 and 21 have an LCM of 273.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13 and 21, than apply into the LCM equation.

GCF(13,21) = 1
LCM(13,21) = ( 13 × 21) / 1
LCM(13,21) = 273 / 1
LCM(13,21) = 273

1. What is the LCM of 13 and 21?

The LCM of 13 and 21 is 273.

2. How to find the lowest common multiple of 13 and 21?

To find the lowest common multiple of 13 and 21, we have to get the multip;es of both numbers and identify the least common multiple in them which is 273.

3. What are the Factors of 13?

Answer: Factors of 13 are 1, 13. There are 2 integers that are factors of 13. The greatest factor of 13 is 13.

4. What are the Factors of 21?

Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.

Answer:

Least Common Multiple of 13 and 21 = 273

Step 1: Find the prime factorization of 13

13 = 13

Step 2: Find the prime factorization of 21

21 = 3 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 = 273 = 3 x 7 x 13

Step 4: Therefore, the least common multiple of 13 and 21 is 273.