Least Common Multiple of 2 and 3

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

• Least Common Multiple of 2 and 3 by Prime method
• Least Common Multiple of 2 and 3 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 2 and 3. First we will calculate the prime factors of 2 and 3.

Prime Factorization of 2

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

2 = 2¹

Prime Factorization of 3

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

3 = 3¹

Now multiplying the highest exponent prime factors to calculate the LCM of 2 and 3.

LCM(2,3) = 2¹×3¹
LCM(2,3) = 6

Factors of 2

List of positive integer factors of 2 that divides 2 without a remainder.

1, 2

Factors of 3

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

1, 3

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2 and 3, than apply into the LCM equation.

GCF(2,3) = 1
LCM(2,3) = ( 2 × 3) / 1
LCM(2,3) = 6 / 1
LCM(2,3) = 6

(i) The LCM of 3 and 2 is associative

LCM of 2 and 3 = LCM of 3 and 2

1. What is the LCM of 2 and 3?

Answer: LCM of 2 and 3 is 6.

2. What are the Factors of 2?

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

3. 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.

4. How to Find the LCM of 2 and 3?

Answer:

Least Common Multiple of 2 and 3 = 6

Step 1: Find the prime factorization of 2

2 = 2

Step 2: Find the prime factorization of 3

3 = 3

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

LCM = 6 = 2 x 3

Step 4: Therefore, the least common multiple of 2 and 3 is 6.