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 nonzero 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) = 3^{1} and (2 × 3) = 2^{1} × 3^{1} respectively. LCM of 3 and 6 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{1} = 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 48 and 60  240
 LCM of 36 and 48  144
 LCM of 14 and 42  42
 LCM of 37 and 49  1813
 LCM of 64 and 96  192
 LCM of 15 and 17  255
 LCM of 40, 42 and 45  2520
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) = 3^{1} and 6 = (2 × 3) = 2^{1} × 3^{1}
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.
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 = 2^{1} × 3^{1} = 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.