Least Common Multiple of 8 and 19

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

• Least Common Multiple of 8 and 19 by Prime method
• Least Common Multiple of 8 and 19 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 19. First we will calculate the prime factors of 8 and 19.

Prime Factorization of 8

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

8 = 2³

Prime Factorization of 19

Prime factors of 19 are 19. Prime factorization of 19 in exponential form is:

19 = 19¹

Now multiplying the highest exponent prime factors to calculate the LCM of 8 and 19.

LCM(8,19) = 2³×19¹
LCM(8,19) = 152

Factors of 8

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

1, 2, 4, 8

Factors of 19

List of positive integer factors of 19 that divides 19 without a remainder.

1, 19

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8 and 19, than apply into the LCM equation.

GCF(8,19) = 1
LCM(8,19) = ( 8 × 19) / 1
LCM(8,19) = 152 / 1
LCM(8,19) = 152

(i) The LCM of 19 and 8 is associative

LCM of 8 and 19 = LCM of 19 and 8

1. What is the LCM of 8 and 19?

Answer: LCM of 8 and 19 is 152.

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 19?

Answer: Factors of 19 are 1, 19. There are 2 integers that are factors of 19. The greatest factor of 19 is 19.

4. How to Find the LCM of 8 and 19?

Answer:

Least Common Multiple of 8 and 19 = 152

Step 1: Find the prime factorization of 8

8 = 2 x 2 x 2

Step 2: Find the prime factorization of 19

19 = 19

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

LCM = 152 = 2 x 2 x 2 x 19

Step 4: Therefore, the least common multiple of 8 and 19 is 152.