Least Common Multiple of 8 and 14

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

• Least Common Multiple of 8 and 14 by Prime method
• Least Common Multiple of 8 and 14 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 14. First we will calculate the prime factors of 8 and 14.

Prime Factorization of 8

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

8 = 2³

Prime Factorization of 14

Prime factors of 14 are 2,7. Prime factorization of 14 in exponential form is:

14 = 2¹×7¹

Now multiplying the highest exponent prime factors to calculate the LCM of 8 and 14.

LCM(8,14) = 2³×7¹
LCM(8,14) = 56

Factors of 8

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

1, 2, 4, 8

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1, 2, 7, 14

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8 and 14, than apply into the LCM equation.

GCF(8,14) = 2
LCM(8,14) = ( 8 × 14) / 2
LCM(8,14) = 112 / 2
LCM(8,14) = 56

(i) The LCM of 14 and 8 is associative

LCM of 8 and 14 = LCM of 14 and 8

1. What is the LCM of 8 and 14?

Answer: LCM of 8 and 14 is 56.

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 14?

Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.

4. How to Find the LCM of 8 and 14?

Answer:

Least Common Multiple of 8 and 14 = 56

Step 1: Find the prime factorization of 8

8 = 2 x 2 x 2

Step 2: Find the prime factorization of 14

14 = 2 x 7

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

LCM = 56 = 2 x 2 x 2 x 7

Step 4: Therefore, the least common multiple of 8 and 14 is 56.