LCM of 3 and 4

LCM of 3 and 4 is the smallest number among all common multiples of 3 and 4. The first few multiples of 3 and 4 are (3, 6, 9, 12, 15, 18, 21, . . . ) and (4, 8, 12, 16, 20, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 4 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 3 and 4 is 12.

Explanation:

The LCM of two non-zero integers, x(3) and y(4), is the smallest positive integer m(12) that is divisible by both x(3) and y(4) without any remainder.

The methods to find the LCM of 3 and 4 are explained below.

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

LCM of 3 and 4 by Listing Multiples

To calculate the LCM of 3 and 4 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 4 (4, 8, 12, 16, 20, . . . . )
• Step 2: The common multiples from the multiples of 3 and 4 are 12, 24, . . .
• Step 3: The smallest common multiple of 3 and 4 is 12.

∴ The least common multiple of 3 and 4 = 12.

LCM of 3 and 4 by Division Method

To calculate the LCM of 3 and 4 by the division method, we will divide the numbers(3, 4) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 4.

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

LCM of 3 and 4 by Prime Factorization

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

☛ Also Check:

• LCM of 60 and 72 - 360
• LCM of 6, 7 and 8 - 168
• LCM of 5, 6 and 10 - 30
• LCM of 8 and 10 - 40
• LCM of 8, 12, 15 and 20 - 120
• LCM of 10 and 100 - 100
• LCM of 8, 12 and 24 - 24

FAQs on LCM of 3 and 4

What is the LCM of 3 and 4?

The LCM of 3 and 4 is 12. To find the LCM of 3 and 4, we need to find the multiples of 3 and 4 (multiples of 3 = 3, 6, 9, 12; multiples of 4 = 4, 8, 12, 16) and choose the smallest multiple that is exactly divisible by 3 and 4, i.e., 12.

What is the Relation Between GCF and LCM of 3, 4?

The following equation can be used to express the relation between GCF and LCM of 3 and 4, i.e. GCF × LCM = 3 × 4.

If the LCM of 4 and 3 is 12, Find its GCF.

LCM(4, 3) × GCF(4, 3) = 4 × 3
Since the LCM of 4 and 3 = 12
⇒ 12 × GCF(4, 3) = 12
Therefore, the greatest common factor (GCF) = 12/12 = 1.

Which of the following is the LCM of 3 and 4? 42, 28, 12, 36

The value of LCM of 3, 4 is the smallest common multiple of 3 and 4. The number satisfying the given condition is 12.

What are the Methods to Find LCM of 3 and 4?

The commonly used methods to find the LCM of 3 and 4 are:

• Listing Multiples
• Prime Factorization Method
• Division Method