Least Common Multiple of 19 and 21

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

• Least Common Multiple of 19 and 21 by Prime method
• Least Common Multiple of 19 and 21 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 19 and 21. First we will calculate the prime factors of 19 and 21.

Prime Factorization of 19

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

19 = 19¹

Prime Factorization of 21

Prime factors of 21 are 3,7. Prime factorization of 21 in exponential form is:

21 = 3¹×7¹

Now multiplying the highest exponent prime factors to calculate the LCM of 19 and 21.

LCM(19,21) = 3¹×7¹×19¹
LCM(19,21) = 399

Factors of 19

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

1, 19

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1, 3, 7, 21

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19 and 21, than apply into the LCM equation.

GCF(19,21) = 1
LCM(19,21) = ( 19 × 21) / 1
LCM(19,21) = 399 / 1
LCM(19,21) = 399

(i) The LCM of 21 and 19 is associative

LCM of 19 and 21 = LCM of 21 and 19

1. What is the LCM of 19 and 21?

Answer: LCM of 19 and 21 is 399.

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 21?

Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.

4. How to Find the LCM of 19 and 21?

Answer:

Least Common Multiple of 19 and 21 = 399

Step 1: Find the prime factorization of 19

19 = 19

Step 2: Find the prime factorization of 21

21 = 3 x 7

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

LCM = 399 = 3 x 7 x 19

Step 4: Therefore, the least common multiple of 19 and 21 is 399.