Least Common Multiple of 3 and 9

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

• Least Common Multiple of 3 and 9 by Prime method
• Least Common Multiple of 3 and 9 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 9. First we will calculate the prime factors of 3 and 9.

Prime Factorization of 3

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

3 = 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 3 and 9.

LCM(3,9) = 3²
LCM(3,9) = 9

Factors of 3

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

1, 3

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 3 and 9, than apply into the LCM equation.

GCF(3,9) = 3
LCM(3,9) = ( 3 × 9) / 3
LCM(3,9) = 27 / 3
LCM(3,9) = 9

(i) The LCM of 9 and 3 is associative

LCM of 3 and 9 = LCM of 9 and 3

1. What is the LCM of 3 and 9?

Answer: LCM of 3 and 9 is 9.

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 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 3 and 9?

Answer:

Least Common Multiple of 3 and 9 = 9

Step 1: Find the prime factorization of 3

3 = 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 = 9 = 3 x 3

Step 4: Therefore, the least common multiple of 3 and 9 is 9.