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LCM of 6 and 12

LCM of 6 and 12 is the smallest number among all common multiples of 6 and 12. The first few multiples of 6 and 12 are (6, 12, 18, 24, . . . ) and (12, 24, 36, 48, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 12 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 6 and 12
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 6 and 12?

Answer: LCM of 6 and 12 is 12.

Explanation:

The LCM of two non-zero integers, x(6) and y(12), is the smallest positive integer m(12) that is divisible by both x(6) and y(12) without any remainder.

Methods to Find LCM of 6 and 12

The methods to find the LCM of 6 and 12 are explained below.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 6 and 12 by Prime Factorization

Prime factorization of 6 and 12 is (2 × 3) = 2¹ × 3¹ and (2 × 2 × 3) = 2² × 3¹ respectively. LCM of 6 and 12 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ = 12.
Hence, the LCM of 6 and 12 by prime factorization is 12.

LCM of 6 and 12 by Listing Multiples

To calculate the LCM of 6 and 12 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 6 (6, 12, 18, 24, . . . ) and 12 (12, 24, 36, 48, . . . . )
Step 2: The common multiples from the multiples of 6 and 12 are 12, 24, . . .
Step 3: The smallest common multiple of 6 and 12 is 12.

∴ The least common multiple of 6 and 12 = 12.

LCM of 6 and 12 by Division Method

To calculate the LCM of 6 and 12 by the division method, we will divide the numbers(6, 12) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 12.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 12. Write this prime number(2) on the left of the given numbers(6 and 12), separated as per the ladder arrangement.
Step 2: If any of the given numbers (6, 12) 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 6 and 12 is the product of all prime numbers on the left, i.e. LCM(6, 12) by division method = 2 × 2 × 3 = 12.

☛ Also Check:

LCM of 6 and 12 Examples

Example 1: The product of two numbers is 72. If their GCD is 6, what is their LCM?

Solution:

Given: GCD = 6
product of numbers = 72
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 72/6
Therefore, the LCM is 12.
The probable combination for the given case is LCM(6, 12) = 12.
Example 2: The GCD and LCM of two numbers are 6 and 12 respectively. If one number is 6, find the other number.

Solution:

Let the other number be a.
∵ GCD × LCM = 6 × a
⇒ a = (GCD × LCM)/6
⇒ a = (6 × 12)/6
⇒ a = 12
Therefore, the other number is 12.
Example 3: Verify the relationship between GCF and LCM of 6 and 12.

Solution:

The relation between GCF and LCM of 6 and 12 is given as,
LCM(6, 12) × GCF(6, 12) = Product of 6, 12
Prime factorization of 6 and 12 is given as, 6 = (2 × 3) = 2¹ × 3¹ and 12 = (2 × 2 × 3) = 2² × 3¹
LCM(6, 12) = 12
GCF(6, 12) = 6
LHS = LCM(6, 12) × GCF(6, 12) = 12 × 6 = 72
RHS = Product of 6, 12 = 6 × 12 = 72
⇒ LHS = RHS = 72
Hence, verified.

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FAQs on LCM of 6 and 12

What is the LCM of 6 and 12?

The LCM of 6 and 12 is 12. To find the least common multiple of 6 and 12, we need to find the multiples of 6 and 12 (multiples of 6 = 6, 12, 18, 24; multiples of 12 = 12, 24, 36, 48) and choose the smallest multiple that is exactly divisible by 6 and 12, i.e., 12.

What are the Methods to Find LCM of 6 and 12?

The commonly used methods to find the LCM of 6 and 12 are:

Listing Multiples
Division Method
Prime Factorization Method

How to Find the LCM of 6 and 12 by Prime Factorization?

To find the LCM of 6 and 12 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (12 = 2 × 2 × 3). LCM of 6 and 12 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 12.
⇒ LCM of 6, 12 = 2² × 3¹ = 12.

Which of the following is the LCM of 6 and 12? 20, 12, 32, 3

The value of LCM of 6, 12 is the smallest common multiple of 6 and 12. The number satisfying the given condition is 12.

If the LCM of 12 and 6 is 12, Find its GCF.

LCM(12, 6) × GCF(12, 6) = 12 × 6
Since the LCM of 12 and 6 = 12
⇒ 12 × GCF(12, 6) = 72
Therefore, the GCF (greatest common factor) = 72/12 = 6.

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