Least Common Multiple of 19 and 22

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

• Least Common Multiple of 19 and 22 by Prime method
• Least Common Multiple of 19 and 22 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 19 and 22. First we will calculate the prime factors of 19 and 22.

Prime Factorization of 19

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

19 = 19¹

Prime Factorization of 22

Prime factors of 22 are 2,11. Prime factorization of 22 in exponential form is:

22 = 2¹×11¹

Now multiplying the highest exponent prime factors to calculate the LCM of 19 and 22.

LCM(19,22) = 2¹×11¹×19¹
LCM(19,22) = 418

Factors of 19

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

1, 19

Factors of 22

List of positive integer factors of 22 that divides 22 without a remainder.

1, 2, 11, 22

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19 and 22, than apply into the LCM equation.

GCF(19,22) = 1
LCM(19,22) = ( 19 × 22) / 1
LCM(19,22) = 418 / 1
LCM(19,22) = 418

(i) The LCM of 22 and 19 is associative

LCM of 19 and 22 = LCM of 22 and 19

1. What is the LCM of 19 and 22?

Answer: LCM of 19 and 22 is 418.

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 22?

Answer: Factors of 22 are 1, 2, 11, 22. There are 4 integers that are factors of 22. The greatest factor of 22 is 22.

4. How to Find the LCM of 19 and 22?

Answer:

Least Common Multiple of 19 and 22 = 418

Step 1: Find the prime factorization of 19

19 = 19

Step 2: Find the prime factorization of 22

22 = 2 x 11

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

LCM = 418 = 2 x 11 x 19

Step 4: Therefore, the least common multiple of 19 and 22 is 418.