Least Common Multiple of 3 and 4

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

• Least Common Multiple of 3 and 4 by Prime method
• Least Common Multiple of 3 and 4 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 4. First we will calculate the prime factors of 3 and 4.

Prime Factorization of 3

Prime factors of 3 are 3. Prime factorization of 3 in exponential form is:

3 = 3¹

Prime Factorization of 4

Prime factors of 4 are 2. Prime factorization of 4 in exponential form is:

4 = 2²

Now multiplying the highest exponent prime factors to calculate the LCM of 3 and 4.

LCM(3,4) = 2²×3¹
LCM(3,4) = 12

Factors of 3

List of positive integer factors of 3 that divides 3 without a remainder.

1, 3

Factors of 4

List of positive integer factors of 4 that divides 4 without a remainder.

1, 2, 4

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3 and 4, than apply into the LCM equation.

GCF(3,4) = 1
LCM(3,4) = ( 3 × 4) / 1
LCM(3,4) = 12 / 1
LCM(3,4) = 12

(i) The LCM of 4 and 3 is associative

LCM of 3 and 4 = LCM of 4 and 3

1. What is the LCM of 3 and 4?

Answer: LCM of 3 and 4 is 12.

2. What are the Factors of 3?

Answer: Factors of 3 are 1, 3. There are 2 integers that are factors of 3. The greatest factor of 3 is 3.

3. What are the Factors of 4?

Answer: Factors of 4 are 1, 2, 4. There are 3 integers that are factors of 4. The greatest factor of 4 is 4.

4. How to Find the LCM of 3 and 4?

Answer:

Least Common Multiple of 3 and 4 = 12

Step 1: Find the prime factorization of 3

3 = 3

Step 2: Find the prime factorization of 4

4 = 2 x 2

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 12 = 2 x 2 x 3

Step 4: Therefore, the least common multiple of 3 and 4 is 12.