Least Common Multiple of 8 and 25

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

• Least Common Multiple of 8 and 25 by Prime method
• Least Common Multiple of 8 and 25 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 25. First we will calculate the prime factors of 8 and 25.

Prime Factorization of 8

Prime factors of 8 are 2. Prime factorization of 8 in exponential form is:

8 = 2³

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 8 and 25.

LCM(8,25) = 2³×5²
LCM(8,25) = 200

Factors of 8

List of positive integer factors of 8 that divides 8 without a remainder.

1, 2, 4, 8

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 8 and 25, than apply into the LCM equation.

GCF(8,25) = 1
LCM(8,25) = ( 8 × 25) / 1
LCM(8,25) = 200 / 1
LCM(8,25) = 200

(i) The LCM of 25 and 8 is associative

LCM of 8 and 25 = LCM of 25 and 8

1. What is the LCM of 8 and 25?

Answer: LCM of 8 and 25 is 200.

2. What are the Factors of 8?

Answer: Factors of 8 are 1, 2, 4, 8. There are 4 integers that are factors of 8. The greatest factor of 8 is 8.

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 8 and 25?

Answer:

Least Common Multiple of 8 and 25 = 200

Step 1: Find the prime factorization of 8

8 = 2 x 2 x 2

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 = 200 = 2 x 2 x 2 x 5 x 5

Step 4: Therefore, the least common multiple of 8 and 25 is 200.