Least Common Multiple of 8 and 12

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

• Least Common Multiple of 8 and 12 by Prime method
• Least Common Multiple of 8 and 12 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 12. First we will calculate the prime factors of 8 and 12.

Prime Factorization of 8

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

8 = 2³

Prime Factorization of 12

Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:

12 = 2²×3¹

Now multiplying the highest exponent prime factors to calculate the LCM of 8 and 12.

LCM(8,12) = 2³×3¹
LCM(8,12) = 24

Factors of 8

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

1, 2, 4, 8

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1, 2, 3, 4, 6, 12

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8 and 12, than apply into the LCM equation.

GCF(8,12) = 4
LCM(8,12) = ( 8 × 12) / 4
LCM(8,12) = 96 / 4
LCM(8,12) = 24

(i) The LCM of 12 and 8 is associative

LCM of 8 and 12 = LCM of 12 and 8

1. What is the LCM of 8 and 12?

Answer: LCM of 8 and 12 is 24.

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 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

4. How to Find the LCM of 8 and 12?

Answer:

Least Common Multiple of 8 and 12 = 24

Step 1: Find the prime factorization of 8

8 = 2 x 2 x 2

Step 2: Find the prime factorization of 12

12 = 2 x 2 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 = 24 = 2 x 2 x 2 x 3

Step 4: Therefore, the least common multiple of 8 and 12 is 24.