Least Common Multiple of 9 and 25

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

• Least Common Multiple of 9 and 25 by Prime method
• Least Common Multiple of 9 and 25 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 25. First we will calculate the prime factors of 9 and 25.

Prime Factorization of 9

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

9 = 3²

Prime Factorization of 25

Prime factors of 25 are 5. Prime factorization of 25 in exponential form is:

25 = 5²

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 25.

LCM(9,25) = 3²×5²
LCM(9,25) = 225

Factors of 9

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

1, 3, 9

Factors of 25

List of positive integer factors of 25 that divides 25 without a remainder.

1, 5, 25

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 25, than apply into the LCM equation.

GCF(9,25) = 1
LCM(9,25) = ( 9 × 25) / 1
LCM(9,25) = 225 / 1
LCM(9,25) = 225

(i) The LCM of 25 and 9 is associative

LCM of 9 and 25 = LCM of 25 and 9

1. What is the LCM of 9 and 25?

Answer: LCM of 9 and 25 is 225.

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 25?

Answer: Factors of 25 are 1, 5, 25. There are 3 integers that are factors of 25. The greatest factor of 25 is 25.

4. How to Find the LCM of 9 and 25?

Answer:

Least Common Multiple of 9 and 25 = 225

Step 1: Find the prime factorization of 9

9 = 3 x 3

Step 2: Find the prime factorization of 25

25 = 5 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 = 225 = 3 x 3 x 5 x 5

Step 4: Therefore, the least common multiple of 9 and 25 is 225.