Least Common Multiple of 9 and 15

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

• Least Common Multiple of 9 and 15 by Prime method
• Least Common Multiple of 9 and 15 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 15. First we will calculate the prime factors of 9 and 15.

Prime Factorization of 9

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

9 = 3²

Prime Factorization of 15

Prime factors of 15 are 3,5. Prime factorization of 15 in exponential form is:

15 = 3¹×5¹

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 15.

LCM(9,15) = 3²×5¹
LCM(9,15) = 45

Factors of 9

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

1, 3, 9

Factors of 15

List of positive integer factors of 15 that divides 15 without a remainder.

1, 3, 5, 15

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 15, than apply into the LCM equation.

GCF(9,15) = 3
LCM(9,15) = ( 9 × 15) / 3
LCM(9,15) = 135 / 3
LCM(9,15) = 45

(i) The LCM of 15 and 9 is associative

LCM of 9 and 15 = LCM of 15 and 9

1. What is the LCM of 9 and 15?

Answer: LCM of 9 and 15 is 45.

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 15?

Answer: Factors of 15 are 1, 3, 5, 15. There are 4 integers that are factors of 15. The greatest factor of 15 is 15.

4. How to Find the LCM of 9 and 15?

Answer:

Least Common Multiple of 9 and 15 = 45

Step 1: Find the prime factorization of 9

9 = 3 x 3

Step 2: Find the prime factorization of 15

15 = 3 x 5

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 45 = 3 x 3 x 5

Step 4: Therefore, the least common multiple of 9 and 15 is 45.