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LCM of 3 and 6

LCM of 3 and 6 is the smallest number among all common multiples of 3 and 6. The first few multiples of 3 and 6 are (3, 6, 9, 12, 15, 18, 21, . . . ) and (6, 12, 18, 24, 30, 36, 42, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 6 - by listing multiples, by division method, and by prime factorization.

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

What is the LCM of 3 and 6?

Answer: LCM of 3 and 6 is 6.

Explanation:

The LCM of two non-zero integers, x(3) and y(6), is the smallest positive integer m(6) that is divisible by both x(3) and y(6) without any remainder.

Methods to Find LCM of 3 and 6

Let's look at the different methods for finding the LCM of 3 and 6.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 3 and 6 by Prime Factorization

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

LCM of 3 and 6 by Listing Multiples

To calculate the LCM of 3 and 6 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 3 (3, 6, 9, 12, 15, 18, 21, . . . ) and 6 (6, 12, 18, 24, 30, 36, 42, . . . . )
Step 2: The common multiples from the multiples of 3 and 6 are 6, 12, . . .
Step 3: The smallest common multiple of 3 and 6 is 6.

∴ The least common multiple of 3 and 6 = 6.

LCM of 3 and 6 by Division Method

To calculate the LCM of 3 and 6 by the division method, we will divide the numbers(3, 6) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 6.

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

☛ Also Check:

LCM of 3 and 6 Examples

Example 1: Verify the relationship between GCF and LCM of 3 and 6.

Solution:

The relation between GCF and LCM of 3 and 6 is given as,
LCM(3, 6) × GCF(3, 6) = Product of 3, 6
Prime factorization of 3 and 6 is given as, 3 = (3) = 3¹ and 6 = (2 × 3) = 2¹ × 3¹
LCM(3, 6) = 6
GCF(3, 6) = 3
LHS = LCM(3, 6) × GCF(3, 6) = 6 × 3 = 18
RHS = Product of 3, 6 = 3 × 6 = 18
⇒ LHS = RHS = 18
Hence, verified.
Example 2: The product of two numbers is 18. If their GCD is 3, what is their LCM?

Solution:

Given: GCD = 3
product of numbers = 18
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 18/3
Therefore, the LCM is 6.
The probable combination for the given case is LCM(3, 6) = 6.
Example 3: Find the smallest number that is divisible by 3 and 6 exactly.

Solution:

The smallest number that is divisible by 3 and 6 exactly is their LCM.
⇒ Multiples of 3 and 6:
- Multiples of 3 = 3, 6, 9, 12, 15, . . . .
- Multiples of 6 = 6, 12, 18, 24, 30, . . . .
Therefore, the LCM of 3 and 6 is 6.

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FAQs on LCM of 3 and 6

What is the LCM of 3 and 6?

The LCM of 3 and 6 is 6. To find the LCM (least common multiple) of 3 and 6, we need to find the multiples of 3 and 6 (multiples of 3 = 3, 6, 9, 12; multiples of 6 = 6, 12, 18, 24) and choose the smallest multiple that is exactly divisible by 3 and 6, i.e., 6.

What is the Least Perfect Square Divisible by 3 and 6?

The least number divisible by 3 and 6 = LCM(3, 6)
LCM of 3 and 6 = 2 × 3 [Incomplete pair(s): 2, 3]
⇒ Least perfect square divisible by each 3 and 6 = LCM(3, 6) × 2 × 3 = 36 [Square root of 36 = √36 = ±6]
Therefore, 36 is the required number.

How to Find the LCM of 3 and 6 by Prime Factorization?

To find the LCM of 3 and 6 using prime factorization, we will find the prime factors, (3 = 3) and (6 = 2 × 3). LCM of 3 and 6 is the product of prime factors raised to their respective highest exponent among the numbers 3 and 6.
⇒ LCM of 3, 6 = 2¹ × 3¹ = 6.

If the LCM of 6 and 3 is 6, Find its GCF.

LCM(6, 3) × GCF(6, 3) = 6 × 3
Since the LCM of 6 and 3 = 6
⇒ 6 × GCF(6, 3) = 18
Therefore, the greatest common factor = 18/6 = 3.

What is the Relation Between GCF and LCM of 3, 6?

The following equation can be used to express the relation between GCF and LCM of 3 and 6, i.e. GCF × LCM = 3 × 6.

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