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LCM of 2 and 14

LCM of 2 and 14 is the smallest number among all common multiples of 2 and 14. The first few multiples of 2 and 14 are (2, 4, 6, 8, 10, . . . ) and (14, 28, 42, 56, 70, . . . ) respectively. There are 3 commonly used methods to find LCM of 2 and 14 - by prime factorization, by listing multiples, and by division method.

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

What is the LCM of 2 and 14?

Answer: LCM of 2 and 14 is 14.

Explanation:

The LCM of two non-zero integers, x(2) and y(14), is the smallest positive integer m(14) that is divisible by both x(2) and y(14) without any remainder.

Methods to Find LCM of 2 and 14

The methods to find the LCM of 2 and 14 are explained below.

By Prime Factorization Method
By Division Method
By Listing Multiples

LCM of 2 and 14 by Prime Factorization

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

LCM of 2 and 14 by Division Method

To calculate the LCM of 2 and 14 by the division method, we will divide the numbers(2, 14) by their prime factors (preferably common). The product of these divisors gives the LCM of 2 and 14.

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

LCM of 2 and 14 by Listing Multiples

To calculate the LCM of 2 and 14 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 2 (2, 4, 6, 8, 10, . . . ) and 14 (14, 28, 42, 56, 70, . . . . )
Step 2: The common multiples from the multiples of 2 and 14 are 14, 28, . . .
Step 3: The smallest common multiple of 2 and 14 is 14.

∴ The least common multiple of 2 and 14 = 14.

☛ Also Check:

LCM of 2 and 14 Examples

Example 1: The product of two numbers is 28. If their GCD is 2, what is their LCM?

Solution:

Given: GCD = 2
product of numbers = 28
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 28/2
Therefore, the LCM is 14.
The probable combination for the given case is LCM(2, 14) = 14.
Example 2: Verify the relationship between GCF and LCM of 2 and 14.

Solution:

The relation between GCF and LCM of 2 and 14 is given as,
LCM(2, 14) × GCF(2, 14) = Product of 2, 14
Prime factorization of 2 and 14 is given as, 2 = (2) = 2¹ and 14 = (2 × 7) = 2¹ × 7¹
LCM(2, 14) = 14
GCF(2, 14) = 2
LHS = LCM(2, 14) × GCF(2, 14) = 14 × 2 = 28
RHS = Product of 2, 14 = 2 × 14 = 28
⇒ LHS = RHS = 28
Hence, verified.
Example 3: Find the smallest number that is divisible by 2 and 14 exactly.

Solution:

The smallest number that is divisible by 2 and 14 exactly is their LCM.
⇒ Multiples of 2 and 14:
- Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, . . . .
- Multiples of 14 = 14, 28, 42, 56, 70, 84, . . . .
Therefore, the LCM of 2 and 14 is 14.

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FAQs on LCM of 2 and 14

What is the LCM of 2 and 14?

The LCM of 2 and 14 is 14. To find the LCM (least common multiple) of 2 and 14, we need to find the multiples of 2 and 14 (multiples of 2 = 2, 4, 6, 8 . . . . 14; multiples of 14 = 14, 28, 42, 56) and choose the smallest multiple that is exactly divisible by 2 and 14, i.e., 14.

Which of the following is the LCM of 2 and 14? 45, 36, 25, 14

The value of LCM of 2, 14 is the smallest common multiple of 2 and 14. The number satisfying the given condition is 14.

How to Find the LCM of 2 and 14 by Prime Factorization?

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

What is the Relation Between GCF and LCM of 2, 14?

The following equation can be used to express the relation between GCF and LCM of 2 and 14, i.e. GCF × LCM = 2 × 14.

If the LCM of 14 and 2 is 14, Find its GCF.

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

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