Least Common Multiple of 12 and 19

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

• Least Common Multiple of 12 and 19 by Prime method
• Least Common Multiple of 12 and 19 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 12 and 19. First we will calculate the prime factors of 12 and 19.

Prime Factorization of 12

Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:

12 = 2²×3¹

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 12 and 19.

LCM(12,19) = 2²×3¹×19¹
LCM(12,19) = 228

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1, 2, 3, 4, 6, 12

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 12 and 19, than apply into the LCM equation.

GCF(12,19) = 1
LCM(12,19) = ( 12 × 19) / 1
LCM(12,19) = 228 / 1
LCM(12,19) = 228

(i) The LCM of 19 and 12 is associative

LCM of 12 and 19 = LCM of 19 and 12

1. What is the LCM of 12 and 19?

Answer: LCM of 12 and 19 is 228.

2. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

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 12 and 19?

Answer:

Least Common Multiple of 12 and 19 = 228

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 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 = 228 = 2 x 2 x 3 x 19

Step 4: Therefore, the least common multiple of 12 and 19 is 228.