What is the LCM of 14 and 14?

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 5 and 14 is 70.

LCM(5,14) = 70

Least Common Multiple of 5 and 14 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5 and 14, than apply into the LCM equation.

GCF(5,14) = 1 LCM(5,14) = ( 5 × 14) / 1 LCM(5,14) = 70 / 1

LCM(5,14) = 70

Least Common Multiple (LCM) of 5 and 14 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5 and 14. First we will calculate the prime factors of 5 and 14.

Prime Factorization of 5

Prime factors of 5 are 5. Prime factorization of 5 in exponential form is:

5 = 51

Prime Factorization of 14

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

14 = 21 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 5 and 14.

LCM(5,14) = 51 × 21 × 71
LCM(5,14) = 70

Least Common Multiple (LCM) of 14 and 14

Step 1) First we find and list the prime factors of 14 and 14 (Prime Factorization):

Prime Factors of 14: 2, 7 Prime Factors of 14: 2, 7 Step 2) Then we look at the frequency of the prime factors as they appear in each set above. List each prime factor the greatest number of times it occurs in either sets:

2, 7 Step 3) Finally, we multiply the prime numbers from Step 2 together.

2 x 7 = 14 That's it. The Least Common Multiple (LCM) of 14 and 14 is 14.

Least Common Multiple (LCM) of 14 and 15

The first step to this method of finding the Least Common Multiple of 14 and 21 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number.

Let’s take a look at the multiples for each of these numbers, 14 and 21:

What are the Multiples of 14?

What are the Multiples of 21?

Let’s take a look at the first 10 multiples for each of these numbers, 14 and 21:

First 10 Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140

First 10 Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210

You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 14 and 21 are 42, 84, 126. Because 42 is the smallest, it is the least common multiple.

The LCM of 14 and 21 is 42.

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.

LCM of 14 and 21 is the smallest number among all common multiples of 14 and 21. The first few multiples of 14 and 21 are (14, 28, 42, 56, . . . ) and (21, 42, 63, 84, . . . ) respectively. There are 3 commonly used methods to find LCM of 14 and 21 - by listing multiples, by prime factorization, and by division method.

What is the LCM of 14 and 21?

Answer: LCM of 14 and 21 is 42.

Explanation:

The LCM of two non-zero integers, x(14) and y(21), is the smallest positive integer m(42) that is divisible by both x(14) and y(21) without any remainder.

Methods to Find LCM of 14 and 21

Let's look at the different methods for finding the LCM of 14 and 21.

• By Prime Factorization Method
• By Listing Multiples
• By Division Method

LCM of 14 and 21 by Prime Factorization

Prime factorization of 14 and 21 is (2 × 7) = 21 × 71 and (3 × 7) = 31 × 71 respectively. LCM of 14 and 21 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 31 × 71 = 42.
Hence, the LCM of 14 and 21 by prime factorization is 42.

LCM of 14 and 21 by Listing Multiples

To calculate the LCM of 14 and 21 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 14 (14, 28, 42, 56, . . . ) and 21 (21, 42, 63, 84, . . . . )
• Step 2: The common multiples from the multiples of 14 and 21 are 42, 84, . . .
• Step 3: The smallest common multiple of 14 and 21 is 42.

∴ The least common multiple of 14 and 21 = 42.

LCM of 14 and 21 by Division Method

To calculate the LCM of 14 and 21 by the division method, we will divide the numbers(14, 21) by their prime factors (preferably common). The product of these divisors gives the LCM of 14 and 21.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 14 and 21. Write this prime number(2) on the left of the given numbers(14 and 21), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (14, 21) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
• Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 14 and 21 is the product of all prime numbers on the left, i.e. LCM(14, 21) by division method = 2 × 3 × 7 = 42.

☛ Also Check:

LCM of 14 and 21 Examples

1. Example 1: The GCD and LCM of two numbers are 7 and 42 respectively. If one number is 21, find the other number.

   Solution:

   Let the other number be m.
   ∵ GCD × LCM = 21 × m ⇒ m = (GCD × LCM)/21 ⇒ m = (7 × 42)/21 ⇒ m = 14

   Therefore, the other number is 14.

Show Solution >

go to slidego to slidego to slide

The LCM of 14 and 21 is 42. To find the least common multiple (LCM) of 14 and 21, we need to find the multiples of 14 and 21 (multiples of 14 = 14, 28, 42, 56; multiples of 21 = 21, 42, 63, 84) and choose the smallest multiple that is exactly divisible by 14 and 21, i.e., 42.

Which of the following is the LCM of 14 and 21? 11, 3, 12, 42

The value of LCM of 14, 21 is the smallest common multiple of 14 and 21. The number satisfying the given condition is 42.

How to Find the LCM of 14 and 21 by Prime Factorization?

To find the LCM of 14 and 21 using prime factorization, we will find the prime factors, (14 = 2 × 7) and (21 = 3 × 7). LCM of 14 and 21 is the product of prime factors raised to their respective highest exponent among the numbers 14 and 21.
⇒ LCM of 14, 21 = 21 × 31 × 71 = 42.

What is the Least Perfect Square Divisible by 14 and 21?

The least number divisible by 14 and 21 = LCM(14, 21) LCM of 14 and 21 = 2 × 3 × 7 [Incomplete pair(s): 2, 3, 7]

⇒ Least perfect square divisible by each 14 and 21 = LCM(14, 21) × 2 × 3 × 7 = 1764 [Square root of 1764 = √1764 = ±42]

If the LCM of 21 and 14 is 42, Find its GCF.

LCM(21, 14) × GCF(21, 14) = 21 × 14 Since the LCM of 21 and 14 = 42 ⇒ 42 × GCF(21, 14) = 294

Therefore, the GCF = 294/42 = 7.