Least Common Multiple of 6 and 8

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

• Least Common Multiple of 6 and 8 by Prime method
• Least Common Multiple of 6 and 8 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 8. First we will calculate the prime factors of 6 and 8.

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 8

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

8 = 2³

Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 8.

LCM(6,8) = 2³×3¹
LCM(6,8) = 24

Factors of 6

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

1, 2, 3, 6

Factors of 8

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

1, 2, 4, 8

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 8, than apply into the LCM equation.

GCF(6,8) = 2
LCM(6,8) = ( 6 × 8) / 2
LCM(6,8) = 48 / 2
LCM(6,8) = 24

(i) The LCM of 8 and 6 is associative

LCM of 6 and 8 = LCM of 8 and 6

1. What is the LCM of 6 and 8?

Answer: LCM of 6 and 8 is 24.

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 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.

4. How to Find the LCM of 6 and 8?

Answer:

Least Common Multiple of 6 and 8 = 24

Step 1: Find the prime factorization of 6

6 = 2 x 3

Step 2: Find the prime factorization of 8

8 = 2 x 2 x 2

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 24 = 2 x 2 x 2 x 3

Step 4: Therefore, the least common multiple of 6 and 8 is 24.