LCM of 2 and 3
LCM of 2 and 3 is the smallest number among all common multiples of 2 and 3. The first few multiples of 2 and 3 are (2, 4, 6, 8, . . . ) and (3, 6, 9, 12, 15, . . . ) respectively. There are 3 commonly used methods to find LCM of 2 and 3  by division method, by listing multiples, and by prime factorization.
1.  LCM of 2 and 3 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 2 and 3?
Answer: LCM of 2 and 3 is 6.
Explanation:
The LCM of two nonzero integers, x(2) and y(3), is the smallest positive integer m(6) that is divisible by both x(2) and y(3) without any remainder.
Methods to Find LCM of 2 and 3
The methods to find the LCM of 2 and 3 are explained below.
 By Listing Multiples
 By Prime Factorization Method
 By Division Method
LCM of 2 and 3 by Listing Multiples
To calculate the LCM of 2 and 3 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, . . . ) and 3 (3, 6, 9, 12, 15, . . . . )
 Step 2: The common multiples from the multiples of 2 and 3 are 6, 12, . . .
 Step 3: The smallest common multiple of 2 and 3 is 6.
∴ The least common multiple of 2 and 3 = 6.
LCM of 2 and 3 by Prime Factorization
Prime factorization of 2 and 3 is (2) = 2^{1} and (3) = 3^{1} respectively. LCM of 2 and 3 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{1} = 6.
Hence, the LCM of 2 and 3 by prime factorization is 6.
LCM of 2 and 3 by Division Method
To calculate the LCM of 2 and 3 by the division method, we will divide the numbers(2, 3) by their prime factors (preferably common). The product of these divisors gives the LCM of 2 and 3.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 2 and 3. Write this prime number(2) on the left of the given numbers(2 and 3), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (2, 3) 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 3 is the product of all prime numbers on the left, i.e. LCM(2, 3) by division method = 2 × 3 = 6.
☛ Also Check:
 LCM of 2, 5 and 7  70
 LCM of 16 and 24  48
 LCM of 3, 7 and 10  210
 LCM of 5 and 16  80
 LCM of 36 and 84  252
 LCM of 20 and 45  180
 LCM of 35 and 55  385
LCM of 2 and 3 Examples

Example 1: The product of two numbers is 6. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 6
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 6/1
Therefore, the LCM is 6.
The probable combination for the given case is LCM(2, 3) = 6. 
Example 2: Find the smallest number that is divisible by 2 and 3 exactly.
Solution:
The smallest number that is divisible by 2 and 3 exactly is their LCM.
⇒ Multiples of 2 and 3: Multiples of 2 = 2, 4, 6, 8, 10, 12, . . . .
 Multiples of 3 = 3, 6, 9, 12, 15, 18, . . . .
Therefore, the LCM of 2 and 3 is 6.

Example 3: The GCD and LCM of two numbers are 1 and 6 respectively. If one number is 2, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 2 × p
⇒ p = (GCD × LCM)/2
⇒ p = (1 × 6)/2
⇒ p = 3
Therefore, the other number is 3.
FAQs on LCM of 2 and 3
What is the LCM of 2 and 3?
The LCM of 2 and 3 is 6. To find the LCM (least common multiple) of 2 and 3, we need to find the multiples of 2 and 3 (multiples of 2 = 2, 4, 6, 8; multiples of 3 = 3, 6, 9, 12) and choose the smallest multiple that is exactly divisible by 2 and 3, i.e., 6.
What is the Least Perfect Square Divisible by 2 and 3?
The least number divisible by 2 and 3 = LCM(2, 3)
LCM of 2 and 3 = 2 × 3 [Incomplete pair(s): 2, 3]
⇒ Least perfect square divisible by each 2 and 3 = LCM(2, 3) × 2 × 3 = 36 [Square root of 36 = √36 = ±6]
Therefore, 36 is the required number.
What are the Methods to Find LCM of 2 and 3?
The commonly used methods to find the LCM of 2 and 3 are:
 Division Method
 Prime Factorization Method
 Listing Multiples
What is the Relation Between GCF and LCM of 2, 3?
The following equation can be used to express the relation between GCF and LCM of 2 and 3, i.e. GCF × LCM = 2 × 3.
If the LCM of 3 and 2 is 6, Find its GCF.
LCM(3, 2) × GCF(3, 2) = 3 × 2
Since the LCM of 3 and 2 = 6
⇒ 6 × GCF(3, 2) = 6
Therefore, the greatest common factor (GCF) = 6/6 = 1.
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