Least Common Multiple of 25 and 27

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

• Least Common Multiple of 25 and 27 by Prime method
• Least Common Multiple of 25 and 27 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 25 and 27. First we will calculate the prime factors of 25 and 27.

Prime Factorization of 25

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

25 = 5²

Prime Factorization of 27

Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:

27 = 3³

Now multiplying the highest exponent prime factors to calculate the LCM of 25 and 27.

LCM(25,27) = 3³×5²
LCM(25,27) = 675

Factors of 25

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

1, 5, 25

Factors of 27

List of positive integer factors of 27 that divides 27 without a remainder.

1, 3, 9, 27

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 25 and 27, than apply into the LCM equation.

GCF(25,27) = 1
LCM(25,27) = ( 25 × 27) / 1
LCM(25,27) = 675 / 1
LCM(25,27) = 675

(i) The LCM of 27 and 25 is associative

LCM of 25 and 27 = LCM of 27 and 25

1. What is the LCM of 25 and 27?

Answer: LCM of 25 and 27 is 675.

2. 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.

3. What are the Factors of 27?

Answer: Factors of 27 are 1, 3, 9, 27. There are 4 integers that are factors of 27. The greatest factor of 27 is 27.

4. How to Find the LCM of 25 and 27?

Answer:

Least Common Multiple of 25 and 27 = 675

Step 1: Find the prime factorization of 25

25 = 5 x 5

Step 2: Find the prime factorization of 27

27 = 3 x 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 = 675 = 3 x 3 x 3 x 5 x 5

Step 4: Therefore, the least common multiple of 25 and 27 is 675.