Least Common Multiple of 9 and 17

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

• Least Common Multiple of 9 and 17 by Prime method
• Least Common Multiple of 9 and 17 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 17. First we will calculate the prime factors of 9 and 17.

Prime Factorization of 9

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

9 = 3²

Prime Factorization of 17

Prime factors of 17 are 17. Prime factorization of 17 in exponential form is:

17 = 17¹

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 17.

LCM(9,17) = 3²×17¹
LCM(9,17) = 153

Factors of 9

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

1, 3, 9

Factors of 17

List of positive integer factors of 17 that divides 17 without a remainder.

1, 17

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 17, than apply into the LCM equation.

GCF(9,17) = 1
LCM(9,17) = ( 9 × 17) / 1
LCM(9,17) = 153 / 1
LCM(9,17) = 153

(i) The LCM of 17 and 9 is associative

LCM of 9 and 17 = LCM of 17 and 9

1. What is the LCM of 9 and 17?

Answer: LCM of 9 and 17 is 153.

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 17?

Answer: Factors of 17 are 1, 17. There are 2 integers that are factors of 17. The greatest factor of 17 is 17.

4. How to Find the LCM of 9 and 17?

Answer:

Least Common Multiple of 9 and 17 = 153

Step 1: Find the prime factorization of 9

9 = 3 x 3

Step 2: Find the prime factorization of 17

17 = 17

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

LCM = 153 = 3 x 3 x 17

Step 4: Therefore, the least common multiple of 9 and 17 is 153.