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.

Answer: LCM of 2 and 3 is 6.

Explanation:

The LCM of two non-zero 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.

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

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.