Least Common Multiple of 9 and 12

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

• Least Common Multiple of 9 and 12 by Prime method
• Least Common Multiple of 9 and 12 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 12. First we will calculate the prime factors of 9 and 12.

Prime Factorization of 9

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

9 = 3²

Prime Factorization of 12

Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:

12 = 2²×3¹

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 12.

LCM(9,12) = 2²×3²
LCM(9,12) = 36

Factors of 9

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

1, 3, 9

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1, 2, 3, 4, 6, 12

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 12, than apply into the LCM equation.

GCF(9,12) = 3
LCM(9,12) = ( 9 × 12) / 3
LCM(9,12) = 108 / 3
LCM(9,12) = 36

(i) The LCM of 12 and 9 is associative

LCM of 9 and 12 = LCM of 12 and 9

1. What is the LCM of 9 and 12?

Answer: LCM of 9 and 12 is 36.

2. 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.

3. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

4. How to Find the LCM of 9 and 12?

Answer:

Least Common Multiple of 9 and 12 = 36

Step 1: Find the prime factorization of 9

9 = 3 x 3

Step 2: Find the prime factorization of 12

12 = 2 x 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 = 36 = 2 x 2 x 3 x 3

Step 4: Therefore, the least common multiple of 9 and 12 is 36.