Least Common Multiple of 19 and 38

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

• Least Common Multiple of 19 and 38 by Prime method
• Least Common Multiple of 19 and 38 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 19 and 38. First we will calculate the prime factors of 19 and 38.

Prime Factorization of 19

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

19 = 19¹

Prime Factorization of 38

Prime factors of 38 are 2,19. Prime factorization of 38 in exponential form is:

38 = 2¹×19¹

Now multiplying the highest exponent prime factors to calculate the LCM of 19 and 38.

LCM(19,38) = 2¹×19¹
LCM(19,38) = 38

Factors of 19

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

1, 19

Factors of 38

List of positive integer factors of 38 that divides 38 without a remainder.

1, 2, 19, 38

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19 and 38, than apply into the LCM equation.

GCF(19,38) = 19
LCM(19,38) = ( 19 × 38) / 19
LCM(19,38) = 722 / 19
LCM(19,38) = 38

(i) The LCM of 38 and 19 is associative

LCM of 19 and 38 = LCM of 38 and 19

1. What is the LCM of 19 and 38?

Answer: LCM of 19 and 38 is 38.

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 38?

Answer: Factors of 38 are 1, 2, 19, 38. There are 4 integers that are factors of 38. The greatest factor of 38 is 38.

4. How to Find the LCM of 19 and 38?

Answer:

Least Common Multiple of 19 and 38 = 38

Step 1: Find the prime factorization of 19

19 = 19

Step 2: Find the prime factorization of 38

38 = 2 x 19

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

LCM = 38 = 2 x 19

Step 4: Therefore, the least common multiple of 19 and 38 is 38.