LCM of 2 and 6

LCM of 2 and 6 is the smallest number among all common multiples of 2 and 6. The first few multiples of 2 and 6 are (2, 4, 6, 8, . . . ) and (6, 12, 18, 24, 30, 36, 42, . . . ) respectively. There are 3 commonly used methods to find LCM of 2 and 6 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 2 and 6 is 6.

Explanation:

The LCM of two non-zero integers, x(2) and y(6), is the smallest positive integer m(6) that is divisible by both x(2) and y(6) without any remainder.

The methods to find the LCM of 2 and 6 are explained below.

• By Listing Multiples
• By Division Method
• By Prime Factorization Method

LCM of 2 and 6 by Listing Multiples

To calculate the LCM of 2 and 6 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 6 (6, 12, 18, 24, 30, 36, 42, . . . . )
• Step 2: The common multiples from the multiples of 2 and 6 are 6, 12, . . .
• Step 3: The smallest common multiple of 2 and 6 is 6.

∴ The least common multiple of 2 and 6 = 6.

LCM of 2 and 6 by Division Method

To calculate the LCM of 2 and 6 by the division method, we will divide the numbers(2, 6) by their prime factors (preferably common). The product of these divisors gives the LCM of 2 and 6.

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

LCM of 2 and 6 by Prime Factorization

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

☛ Also Check:

• LCM of 8 and 32 - 32
• LCM of 3, 5 and 6 - 30
• LCM of 8 and 9 - 72
• LCM of 36, 48 and 72 - 144
• LCM of 54 and 90 - 270
• LCM of 8 and 11 - 88
• LCM of 4, 5 and 8 - 40

FAQs on LCM of 2 and 6

What is the LCM of 2 and 6?

The LCM of 2 and 6 is 6. To find the least common multiple of 2 and 6, we need to find the multiples of 2 and 6 (multiples of 2 = 2, 4, 6, 8; multiples of 6 = 6, 12, 18, 24) and choose the smallest multiple that is exactly divisible by 2 and 6, i.e., 6.

If the LCM of 6 and 2 is 6, Find its GCF.

LCM(6, 2) × GCF(6, 2) = 6 × 2
Since the LCM of 6 and 2 = 6
⇒ 6 × GCF(6, 2) = 12
Therefore, the greatest common factor (GCF) = 12/6 = 2.

How to Find the LCM of 2 and 6 by Prime Factorization?

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

What is the Relation Between GCF and LCM of 2, 6?

The following equation can be used to express the relation between GCF and LCM of 2 and 6, i.e. GCF × LCM = 2 × 6.

What is the Least Perfect Square Divisible by 2 and 6?

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