Least Common Multiple of 6 and 25

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

• Least Common Multiple of 6 and 25 by Prime method
• Least Common Multiple of 6 and 25 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 25. First we will calculate the prime factors of 6 and 25.

Prime Factorization of 6

Prime factors of 6 are 2,3. Prime factorization of 6 in exponential form is:

6 = 2¹×3¹

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 6 and 25.

LCM(6,25) = 2¹×3¹×5²
LCM(6,25) = 150

Factors of 6

List of positive integer factors of 6 that divides 6 without a remainder.

1, 2, 3, 6

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 6 and 25, than apply into the LCM equation.

GCF(6,25) = 1
LCM(6,25) = ( 6 × 25) / 1
LCM(6,25) = 150 / 1
LCM(6,25) = 150

(i) The LCM of 25 and 6 is associative

LCM of 6 and 25 = LCM of 25 and 6

1. What is the LCM of 6 and 25?

Answer: LCM of 6 and 25 is 150.

2. What are the Factors of 6?

Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.

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 6 and 25?

Answer:

Least Common Multiple of 6 and 25 = 150

Step 1: Find the prime factorization of 6

6 = 2 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 = 150 = 2 x 3 x 5 x 5

Step 4: Therefore, the least common multiple of 6 and 25 is 150.