Least Common Multiple of 3 and 19

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

• Least Common Multiple of 3 and 19 by Prime method
• Least Common Multiple of 3 and 19 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 19. First we will calculate the prime factors of 3 and 19.

Prime Factorization of 3

Prime factors of 3 are 3. Prime factorization of 3 in exponential form is:

3 = 3¹

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 3 and 19.

LCM(3,19) = 3¹×19¹
LCM(3,19) = 57

Factors of 3

List of positive integer factors of 3 that divides 3 without a remainder.

1, 3

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 3 and 19, than apply into the LCM equation.

GCF(3,19) = 1
LCM(3,19) = ( 3 × 19) / 1
LCM(3,19) = 57 / 1
LCM(3,19) = 57

(i) The LCM of 19 and 3 is associative

LCM of 3 and 19 = LCM of 19 and 3

1. What is the LCM of 3 and 19?

Answer: LCM of 3 and 19 is 57.

2. What are the Factors of 3?

Answer: Factors of 3 are 1, 3. There are 2 integers that are factors of 3. The greatest factor of 3 is 3.

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 3 and 19?

Answer:

Least Common Multiple of 3 and 19 = 57

Step 1: Find the prime factorization of 3

3 = 3

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 = 57 = 3 x 19

Step 4: Therefore, the least common multiple of 3 and 19 is 57.