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LCM of 4 and 14

LCM of 4 and 14 is the smallest number among all common multiples of 4 and 14. The first few multiples of 4 and 14 are (4, 8, 12, 16, 20, 24, 28, . . . ) and (14, 28, 42, 56, 70, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 14 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 4 and 14
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 4 and 14?

Answer: LCM of 4 and 14 is 28.

Explanation:

The LCM of two non-zero integers, x(4) and y(14), is the smallest positive integer m(28) that is divisible by both x(4) and y(14) without any remainder.

Methods to Find LCM of 4 and 14

The methods to find the LCM of 4 and 14 are explained below.

By Listing Multiples
By Division Method
By Prime Factorization Method

LCM of 4 and 14 by Listing Multiples

To calculate the LCM of 4 and 14 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 4 (4, 8, 12, 16, 20, 24, 28, . . . ) and 14 (14, 28, 42, 56, 70, . . . . )
Step 2: The common multiples from the multiples of 4 and 14 are 28, 56, . . .
Step 3: The smallest common multiple of 4 and 14 is 28.

∴ The least common multiple of 4 and 14 = 28.

LCM of 4 and 14 by Division Method

To calculate the LCM of 4 and 14 by the division method, we will divide the numbers(4, 14) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 14.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 14. Write this prime number(2) on the left of the given numbers(4 and 14), separated as per the ladder arrangement.
Step 2: If any of the given numbers (4, 14) 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 4 and 14 is the product of all prime numbers on the left, i.e. LCM(4, 14) by division method = 2 × 2 × 7 = 28.

LCM of 4 and 14 by Prime Factorization

Prime factorization of 4 and 14 is (2 × 2) = 2² and (2 × 7) = 2¹ × 7¹ respectively. LCM of 4 and 14 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 7¹ = 28.
Hence, the LCM of 4 and 14 by prime factorization is 28.

☛ Also Check:

LCM of 4 and 14 Examples

Example 1: Verify the relationship between GCF and LCM of 4 and 14.

Solution:

The relation between GCF and LCM of 4 and 14 is given as,
LCM(4, 14) × GCF(4, 14) = Product of 4, 14
Prime factorization of 4 and 14 is given as, 4 = (2 × 2) = 2² and 14 = (2 × 7) = 2¹ × 7¹
LCM(4, 14) = 28
GCF(4, 14) = 2
LHS = LCM(4, 14) × GCF(4, 14) = 28 × 2 = 56
RHS = Product of 4, 14 = 4 × 14 = 56
⇒ LHS = RHS = 56
Hence, verified.
Example 2: The GCD and LCM of two numbers are 2 and 28 respectively. If one number is 14, find the other number.

Solution:

Let the other number be m.
∵ GCD × LCM = 14 × m
⇒ m = (GCD × LCM)/14
⇒ m = (2 × 28)/14
⇒ m = 4
Therefore, the other number is 4.
Example 3: Find the smallest number that is divisible by 4 and 14 exactly.

Solution:

The smallest number that is divisible by 4 and 14 exactly is their LCM.
⇒ Multiples of 4 and 14:
- Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, . . . .
- Multiples of 14 = 14, 28, 42, 56, 70, 84, 98, . . . .
Therefore, the LCM of 4 and 14 is 28.

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FAQs on LCM of 4 and 14

What is the LCM of 4 and 14?

The LCM of 4 and 14 is 28. To find the LCM of 4 and 14, we need to find the multiples of 4 and 14 (multiples of 4 = 4, 8, 12, 16 . . . . 28; multiples of 14 = 14, 28, 42, 56) and choose the smallest multiple that is exactly divisible by 4 and 14, i.e., 28.

How to Find the LCM of 4 and 14 by Prime Factorization?

To find the LCM of 4 and 14 using prime factorization, we will find the prime factors, (4 = 2 × 2) and (14 = 2 × 7). LCM of 4 and 14 is the product of prime factors raised to their respective highest exponent among the numbers 4 and 14.
⇒ LCM of 4, 14 = 2² × 7¹ = 28.

What is the Relation Between GCF and LCM of 4, 14?

The following equation can be used to express the relation between GCF and LCM of 4 and 14, i.e. GCF × LCM = 4 × 14.

Which of the following is the LCM of 4 and 14? 35, 24, 11, 28

The value of LCM of 4, 14 is the smallest common multiple of 4 and 14. The number satisfying the given condition is 28.

If the LCM of 14 and 4 is 28, Find its GCF.

LCM(14, 4) × GCF(14, 4) = 14 × 4
Since the LCM of 14 and 4 = 28
⇒ 28 × GCF(14, 4) = 56
Therefore, the greatest common factor = 56/28 = 2.

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