LCM of 4 and 6

LCM of 4 and 6 is the smallest number among all common multiples of 4 and 6. The first few multiples of 4 and 6 are (4, 8, 12, 16, 20, 24, . . . ) and (6, 12, 18, 24, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 6 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 4 and 6 is 12.

Explanation:

The LCM of two non-zero integers, x(4) and y(6), is the smallest positive integer m(12) that is divisible by both x(4) and y(6) without any remainder.

The methods to find the LCM of 4 and 6 are explained below.

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

LCM of 4 and 6 by Listing Multiples

To calculate the LCM of 4 and 6 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 4 (4, 8, 12, 16, 20, 24, . . . ) and 6 (6, 12, 18, 24, . . . . )
• Step 2: The common multiples from the multiples of 4 and 6 are 12, 24, . . .
• Step 3: The smallest common multiple of 4 and 6 is 12.

∴ The least common multiple of 4 and 6 = 12.

LCM of 4 and 6 by Prime Factorization

Prime factorization of 4 and 6 is (2 × 2) = 2² and (2 × 3) = 2¹ × 3¹ respectively. LCM of 4 and 6 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ = 12.
Hence, the LCM of 4 and 6 by prime factorization is 12.

LCM of 4 and 6 by Division Method

To calculate the LCM of 4 and 6 by the division method, we will divide the numbers(4, 6) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 6.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 6. Write this prime number(2) on the left of the given numbers(4 and 6), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (4, 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 4 and 6 is the product of all prime numbers on the left, i.e. LCM(4, 6) by division method = 2 × 2 × 3 = 12.

☛ Also Check:

• LCM of 8, 15 and 21 - 840
• LCM of 8 and 14 - 56
• LCM of 8, 10 and 15 - 120
• LCM of 2, 3 and 4 - 12
• LCM of 42 and 70 - 210
• LCM of 25 and 30 - 150
• LCM of 7 and 17 - 119

FAQs on LCM of 4 and 6

What is the LCM of 4 and 6?

The LCM of 4 and 6 is 12. To find the least common multiple (LCM) of 4 and 6, we need to find the multiples of 4 and 6 (multiples of 4 = 4, 8, 12, 16; multiples of 6 = 6, 12, 18, 24) and choose the smallest multiple that is exactly divisible by 4 and 6, i.e., 12.

If the LCM of 6 and 4 is 12, Find its GCF.

LCM(6, 4) × GCF(6, 4) = 6 × 4
Since the LCM of 6 and 4 = 12
⇒ 12 × GCF(6, 4) = 24
Therefore, the GCF = 24/12 = 2.

What is the Relation Between GCF and LCM of 4, 6?

The following equation can be used to express the relation between GCF and LCM of 4 and 6, i.e. GCF × LCM = 4 × 6.

What is the Least Perfect Square Divisible by 4 and 6?

The least number divisible by 4 and 6 = LCM(4, 6)
LCM of 4 and 6 = 2 × 2 × 3 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 4 and 6 = LCM(4, 6) × 3 = 36 [Square root of 36 = √36 = ±6]
Therefore, 36 is the required number.

What are the Methods to Find LCM of 4 and 6?

The commonly used methods to find the LCM of 4 and 6 are:

• Prime Factorization Method
• Listing Multiples
• Division Method