Least Common Multiple of 15 and 9

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

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

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

Prime Factorization of 15

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

15 = 3¹×5¹

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 15 and 9.

LCM(15,9) = 3²×5¹
LCM(15,9) = 45

Factors of 15

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

1, 3, 5, 15

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 15 and 9, than apply into the LCM equation.

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

(i) The LCM of 9 and 15 is associative

LCM of 15 and 9 = LCM of 9 and 15

1. What is the LCM of 15 and 9?

Answer: LCM of 15 and 9 is 45.

2. 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.

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 15 and 9?

Answer:

Least Common Multiple of 15 and 9 = 45

Step 1: Find the prime factorization of 15

15 = 3 x 5

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 = 45 = 3 x 3 x 5

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