Given Numbers are 21, 26

We can find the LCM of 21, 26 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 21 and 26

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

Multiples of 26 =26,52,78,104,130,156,182,208,234,260,286,312,338,364,390,416,442,

Now, get the least common multiple of 21, 26 which is 546

So, the LCM of 21, 26 is 546.

One method for determining the LCM of 21 and 26 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 21's prime factorization:

Prime factors of 21 are 3,7.

21 = 3¹×7¹

And this is 26's prime factorization:

Prime factors of 26 are 2,13.

26 = 2¹×13¹

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: 3,7, 2,13

2¹×3¹×7¹×13¹ = 546

This shows that the LCM of 21 and 26 is 546.

The first step in determining the Least Common Multiple of 21 and 26 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 21 and 26:

Lets look at the first ten multiples of these numbers, 21 and 26:

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

26,52,78,104,130,156,182,208,234,442 are the first ten multiples of 26.

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 21 and 26, for example, are 252, 357, and 416. 546 is the least common multiple since it is the smallest.

21 and 26 have an LCM of 546.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21 and 26, than apply into the LCM equation.

GCF(21,26) = 1
LCM(21,26) = ( 21 × 26) / 1
LCM(21,26) = 546 / 1
LCM(21,26) = 546

1. What is the LCM of 21 and 26?

The LCM of 21 and 26 is 546.

2. How to find the lowest common multiple of 21 and 26?

To find the lowest common multiple of 21 and 26, we have to get the multip;es of both numbers and identify the least common multiple in them which is 546.

3. 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.

4. What are the Factors of 26?

Answer: Factors of 26 are 1, 2, 13, 26. There are 4 integers that are factors of 26. The greatest factor of 26 is 26.

Answer:

Least Common Multiple of 21 and 26 = 546

Step 1: Find the prime factorization of 21

21 = 3 x 7

Step 2: Find the prime factorization of 26

26 = 2 x 13

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

LCM = 546 = 2 x 3 x 7 x 13

Step 4: Therefore, the least common multiple of 21 and 26 is 546.