Given Numbers are 14, 21

We can find the LCM of 14, 21 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 14 and 21

Multiples of 14 =14,28,42,56,70,84,98,112,126,140,154,168,182,196,210,224,238,

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 14, 21 which is 42

So, the LCM of 14, 21 is 42.

One method for determining the LCM of 14 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 14's prime factorization:

Prime factors of 14 are 2,7.

14 = 2¹×7¹

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: 2,7,3

2¹×3¹×7¹ = 42

This shows that the LCM of 14 and 21 is 42.

The first step in determining the Least Common Multiple of 14 and 21 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 14 and 21:

Lets look at the first ten multiples of these numbers, 14 and 21:

14,28,42,56,70,84,98,112,126,238 are the first ten multiples of 14.

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 14 and 21, for example, are 168, 238, and 336. 42 is the least common multiple since it is the smallest.

14 and 21 have an LCM of 42.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14 and 21, than apply into the LCM equation.

GCF(14,21) = 7
LCM(14,21) = ( 14 × 21) / 7
LCM(14,21) = 294 / 7
LCM(14,21) = 42

1. What is the LCM of 14 and 21?

The LCM of 14 and 21 is 42.

2. How to find the lowest common multiple of 14 and 21?

To find the lowest common multiple of 14 and 21, we have to get the multip;es of both numbers and identify the least common multiple in them which is 42.

3. What are the Factors of 14?

Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.

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 14 and 21 = 42

Step 1: Find the prime factorization of 14

14 = 2 x 7

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 = 42 = 2 x 3 x 7

Step 4: Therefore, the least common multiple of 14 and 21 is 42.