Least Common Multiple of 5 and 9

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

• Least Common Multiple of 5 and 9 by Prime method
• Least Common Multiple of 5 and 9 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 5 and 9. First we will calculate the prime factors of 5 and 9.

Prime Factorization of 5

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

5 = 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 5 and 9.

LCM(5,9) = 3²×5¹
LCM(5,9) = 45

Factors of 5

List of positive integer factors of 5 that divides 5 without a remainder.

1, 5

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 5 and 9, than apply into the LCM equation.

GCF(5,9) = 1
LCM(5,9) = ( 5 × 9) / 1
LCM(5,9) = 45 / 1
LCM(5,9) = 45

(i) The LCM of 9 and 5 is associative

LCM of 5 and 9 = LCM of 9 and 5

1. What is the LCM of 5 and 9?

Answer: LCM of 5 and 9 is 45.

2. What are the Factors of 5?

Answer: Factors of 5 are 1, 5. There are 2 integers that are factors of 5. The greatest factor of 5 is 5.

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 5 and 9?

Answer:

Least Common Multiple of 5 and 9 = 45

Step 1: Find the prime factorization of 5

5 = 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 5 and 9 is 45.