Least Common Multiple of 19 and 20

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

• Least Common Multiple of 19 and 20 by Prime method
• Least Common Multiple of 19 and 20 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 19 and 20. First we will calculate the prime factors of 19 and 20.

Prime Factorization of 19

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

19 = 19¹

Prime Factorization of 20

Prime factors of 20 are 2,5. Prime factorization of 20 in exponential form is:

20 = 2²×5¹

Now multiplying the highest exponent prime factors to calculate the LCM of 19 and 20.

LCM(19,20) = 2²×5¹×19¹
LCM(19,20) = 380

Factors of 19

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

1, 19

Factors of 20

List of positive integer factors of 20 that divides 20 without a remainder.

1, 2, 4, 5, 10, 20

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19 and 20, than apply into the LCM equation.

GCF(19,20) = 1
LCM(19,20) = ( 19 × 20) / 1
LCM(19,20) = 380 / 1
LCM(19,20) = 380

(i) The LCM of 20 and 19 is associative

LCM of 19 and 20 = LCM of 20 and 19

1. What is the LCM of 19 and 20?

Answer: LCM of 19 and 20 is 380.

2. 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.

3. What are the Factors of 20?

Answer: Factors of 20 are 1, 2, 4, 5, 10, 20. There are 6 integers that are factors of 20. The greatest factor of 20 is 20.

4. How to Find the LCM of 19 and 20?

Answer:

Least Common Multiple of 19 and 20 = 380

Step 1: Find the prime factorization of 19

19 = 19

Step 2: Find the prime factorization of 20

20 = 2 x 2 x 5

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

LCM = 380 = 2 x 2 x 5 x 19

Step 4: Therefore, the least common multiple of 19 and 20 is 380.