What is the lcm of 14 and 21

If you just want to know what is the least common multiple of 14 and 21, it is 42. Usually, this is written as

lcm(14,21) = 42

The lcm of 14 and 21 can be obtained like this:

The multiples of 14 are … , 28, 42, 56, ….
The multiples of 21 are …, 21, 42, 63, …
The common multiples of 14 and 21 are n x 42, intersecting the two sets above, .
In the intersection multiples of 14 ∩ multiples of 21 the least positive element is 42.
Therefore, the least common multiple of 14 and 21 is 42.

Taking the above into account you also know how to find all the common multiples of 14 and 21, not just the smallest. In the next section we show you how to calculate the lcm of fourteen and twenty-one by means of two more methods.

How to find the LCM of 14 and 21

The least common multiple of 14 and 21 can be computed by using the greatest common factor aka gcf of 14 and 21. This is the easiest approach:

lcm (14,21) = = 42

Alternatively, the lcm of 14 and 21 can be found using the prime factorization of 14 and 21:

The prime factorization of 14 is: 2 x 7
The prime factorization of 21 is: 3 x 7
Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(14,14) = 42

In any case, the easiest way to compute the lcm of two numbers like 14 and 21 is by using our calculator below. Note that it can also compute the lcm of more than two numbers, separated by a comma. For example, enter 14,21. Push the button only to start over.

Similar searched terms on our site also include:

LCM of 14 and 26
LCM of 14 and 27
LCM of 14 and 28

Use of LCM of 14 and 21

What is the least common multiple of 14 and 21 used for? Answer: It is helpful for adding and subtracting fractions like 1/14 and 1/21. Just multiply the dividends and divisors by 3 and 2, respectively, such that the divisors have the value of 42, the lcm of 14 and 21.

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Properties of LCM of 14 and 21

The most important properties of the lcm(14,21) are:

Commutative property: lcm(14,21) = lcm(21,14)
Associative property: lcm(14,21,n) = lcm(lcm(21,14),n)

The associativity is particularly useful to get the lcm of three or more numbers; our calculator makes use of it.

To sum up, the lcm of 14 and 21 is 42. In common notation: lcm (14,21) = 42.

If you have been searching for lcm 14 and 21 or lcm 14 21 then you have come to the correct page, too. The same is the true if you typed lcm for 14 and 21 in your favorite search engine.

Note that you can find the least common multiple of many integer pairs including fourteen / twenty-one by using the search form in the sidebar of this page.

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On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 14 and 21.

Follow the steps below, and let's calculate the LCM of 14 and 21.

Method 1 - Prime factorization

Step 1: Create a list of all the prime factors of the numbers 14 and 21:

The prime factors of 14 are 2 and 7. Prime factorization of 14 in exponential form is:

14 = 21x71

The prime factors of 21 are 3 and 7. Prime factorization of 21 in exponential form is:

21 = 31x71

Step 2: Identify the highest power of each prime number from the above boxes:

Step 3: Multiply these values together:

Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 14 and 21.

The Least Common Multiple of 14 and 21 is 42.

Method 2 - List of Multiples

Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.

Multiples of 14:

Multiples of 21:

Therefore,

1. What is the LCM of 14 and 21?

Answer: LCM of 14 and 21 is 42.

2. 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.

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. How to Find the LCM of 14 and 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.

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 14 and 21 is 42.

LCM(14,21) = 42

Least Common Multiple of 14 and 21 with GCF Formula

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

Least Common Multiple (LCM) of 14 and 21 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14 and 21. First we will calculate the prime factors of 14 and 21.

Prime Factorization of 14

Prime factors of 14 are 2, 7. Prime factorization of 14 in exponential form is:

14 = 21 × 71

Prime Factorization of 21

Prime factors of 21 are 3, 7. Prime factorization of 21 in exponential form is:

21 = 31 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 14 and 21.

LCM(14,21) = 21 × 71 × 31
LCM(14,21) = 42

The LCM of 14 and 21 is 42.

Steps to find LCM

Find the prime factorization of 14
14 = 2 × 7
Find the prime factorization of 21
21 = 3 × 7
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:
LCM = 2 × 3 × 7
LCM = 42

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