Least Common Multiple of 3 and 6

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

• Least Common Multiple of 3 and 6 by Prime method
• Least Common Multiple of 3 and 6 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 6. First we will calculate the prime factors of 3 and 6.

Prime Factorization of 3

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

3 = 3¹

Prime Factorization of 6

Prime factors of 6 are 2,3. Prime factorization of 6 in exponential form is:

6 = 2¹×3¹

Now multiplying the highest exponent prime factors to calculate the LCM of 3 and 6.

LCM(3,6) = 2¹×3¹
LCM(3,6) = 6

Factors of 3

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

1, 3

Factors of 6

List of positive integer factors of 6 that divides 6 without a remainder.

1, 2, 3, 6

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3 and 6, than apply into the LCM equation.

GCF(3,6) = 3
LCM(3,6) = ( 3 × 6) / 3
LCM(3,6) = 18 / 3
LCM(3,6) = 6

(i) The LCM of 6 and 3 is associative

LCM of 3 and 6 = LCM of 6 and 3

1. What is the LCM of 3 and 6?

Answer: LCM of 3 and 6 is 6.

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 6?

Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.

4. How to Find the LCM of 3 and 6?

Answer:

Least Common Multiple of 3 and 6 = 6

Step 1: Find the prime factorization of 3

3 = 3

Step 2: Find the prime factorization of 6

6 = 2 x 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 3 and 6 is 6.