Least Common Multiple of 9 and 13

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

• Least Common Multiple of 9 and 13 by Prime method
• Least Common Multiple of 9 and 13 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 13. First we will calculate the prime factors of 9 and 13.

Prime Factorization of 9

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

9 = 3²

Prime Factorization of 13

Prime factors of 13 are 13. Prime factorization of 13 in exponential form is:

13 = 13¹

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 13.

LCM(9,13) = 3²×13¹
LCM(9,13) = 117

Factors of 9

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

1, 3, 9

Factors of 13

List of positive integer factors of 13 that divides 13 without a remainder.

1, 13

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 13, than apply into the LCM equation.

GCF(9,13) = 1
LCM(9,13) = ( 9 × 13) / 1
LCM(9,13) = 117 / 1
LCM(9,13) = 117

(i) The LCM of 13 and 9 is associative

LCM of 9 and 13 = LCM of 13 and 9

1. What is the LCM of 9 and 13?

Answer: LCM of 9 and 13 is 117.

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 13?

Answer: Factors of 13 are 1, 13. There are 2 integers that are factors of 13. The greatest factor of 13 is 13.

4. How to Find the LCM of 9 and 13?

Answer:

Least Common Multiple of 9 and 13 = 117

Step 1: Find the prime factorization of 9

9 = 3 x 3

Step 2: Find the prime factorization of 13

13 = 13

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

LCM = 117 = 3 x 3 x 13

Step 4: Therefore, the least common multiple of 9 and 13 is 117.