Least Common Multiple of 16 and 19

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

• Least Common Multiple of 16 and 19 by Prime method
• Least Common Multiple of 16 and 19 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 16 and 19. First we will calculate the prime factors of 16 and 19.

Prime Factorization of 16

Prime factors of 16 are 2. Prime factorization of 16 in exponential form is:

16 = 2⁴

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 16 and 19.

LCM(16,19) = 2⁴×19¹
LCM(16,19) = 304

Factors of 16

List of positive integer factors of 16 that divides 16 without a remainder.

1, 2, 4, 8, 16

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 16 and 19, than apply into the LCM equation.

GCF(16,19) = 1
LCM(16,19) = ( 16 × 19) / 1
LCM(16,19) = 304 / 1
LCM(16,19) = 304

(i) The LCM of 19 and 16 is associative

LCM of 16 and 19 = LCM of 19 and 16

1. What is the LCM of 16 and 19?

Answer: LCM of 16 and 19 is 304.

2. What are the Factors of 16?

Answer: Factors of 16 are 1, 2, 4, 8, 16. There are 5 integers that are factors of 16. The greatest factor of 16 is 16.

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 16 and 19?

Answer:

Least Common Multiple of 16 and 19 = 304

Step 1: Find the prime factorization of 16

16 = 2 x 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 = 304 = 2 x 2 x 2 x 2 x 19

Step 4: Therefore, the least common multiple of 16 and 19 is 304.