Least Common Multiple of 6 and 9

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

• Least Common Multiple of 6 and 9 by Prime method
• Least Common Multiple of 6 and 9 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 9. First we will calculate the prime factors of 6 and 9.

Prime Factorization of 6

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

6 = 2¹×3¹

Prime Factorization of 9

Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:

9 = 3²

Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 9.

LCM(6,9) = 2¹×3²
LCM(6,9) = 18

Factors of 6

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

1, 2, 3, 6

Factors of 9

List of positive integer factors of 9 that divides 9 without a remainder.

1, 3, 9

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 9, than apply into the LCM equation.

GCF(6,9) = 3
LCM(6,9) = ( 6 × 9) / 3
LCM(6,9) = 54 / 3
LCM(6,9) = 18

(i) The LCM of 9 and 6 is associative

LCM of 6 and 9 = LCM of 9 and 6

1. What is the LCM of 6 and 9?

Answer: LCM of 6 and 9 is 18.

2. 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.

3. What are the Factors of 9?

Answer: Factors of 9 are 1, 3, 9. There are 3 integers that are factors of 9. The greatest factor of 9 is 9.

4. How to Find the LCM of 6 and 9?

Answer:

Least Common Multiple of 6 and 9 = 18

Step 1: Find the prime factorization of 6

6 = 2 x 3

Step 2: Find the prime factorization of 9

9 = 3 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 = 18 = 2 x 3 x 3

Step 4: Therefore, the least common multiple of 6 and 9 is 18.