Least Common Multiple of 14 and 19

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

• Least Common Multiple of 14 and 19 by Prime method
• Least Common Multiple of 14 and 19 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 14 and 19. First we will calculate the prime factors of 14 and 19.

Prime Factorization of 14

Prime factors of 14 are 2,7. Prime factorization of 14 in exponential form is:

14 = 2¹×7¹

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 14 and 19.

LCM(14,19) = 2¹×7¹×19¹
LCM(14,19) = 266

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1, 2, 7, 14

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 14 and 19, than apply into the LCM equation.

GCF(14,19) = 1
LCM(14,19) = ( 14 × 19) / 1
LCM(14,19) = 266 / 1
LCM(14,19) = 266

(i) The LCM of 19 and 14 is associative

LCM of 14 and 19 = LCM of 19 and 14

1. What is the LCM of 14 and 19?

Answer: LCM of 14 and 19 is 266.

2. What are the Factors of 14?

Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.

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 14 and 19?

Answer:

Least Common Multiple of 14 and 19 = 266

Step 1: Find the prime factorization of 14

14 = 2 x 7

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 = 266 = 2 x 7 x 19

Step 4: Therefore, the least common multiple of 14 and 19 is 266.