Least Common Multiple of 9 and 27

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

• Least Common Multiple of 9 and 27 by Prime method
• Least Common Multiple of 9 and 27 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 27. First we will calculate the prime factors of 9 and 27.

Prime Factorization of 9

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

9 = 3²

Prime Factorization of 27

Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:

27 = 3³

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 27.

LCM(9,27) = 3³
LCM(9,27) = 27

Factors of 9

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

1, 3, 9

Factors of 27

List of positive integer factors of 27 that divides 27 without a remainder.

1, 3, 9, 27

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 27, than apply into the LCM equation.

GCF(9,27) = 9
LCM(9,27) = ( 9 × 27) / 9
LCM(9,27) = 243 / 9
LCM(9,27) = 27

(i) The LCM of 27 and 9 is associative

LCM of 9 and 27 = LCM of 27 and 9

1. What is the LCM of 9 and 27?

Answer: LCM of 9 and 27 is 27.

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 27?

Answer: Factors of 27 are 1, 3, 9, 27. There are 4 integers that are factors of 27. The greatest factor of 27 is 27.

4. How to Find the LCM of 9 and 27?

Answer:

Least Common Multiple of 9 and 27 = 27

Step 1: Find the prime factorization of 9

9 = 3 x 3

Step 2: Find the prime factorization of 27

27 = 3 x 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 = 27 = 3 x 3 x 3

Step 4: Therefore, the least common multiple of 9 and 27 is 27.