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Least Common Multiple of 12 and 19

Free LCM Calculator determines the least common multiple (LCM) between 12 and 19 the smallest integer that is 228 that is divisible by both numbers.

Least Common Multiple (LCM) of 12 and 19 is 228.

LCM(12,19) = 228

LCM of 12 and 19

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

LCM of:
and

Least Common Multiple (LCM) of 12 and 19 with Primes

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


2 12
2 6
3 3
1

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

12 = 22×31

Prime Factorization of 19


19 19
1

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

Least Common Multiple of 12 and 19 with GCF Formula

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

Properties of LCM 12 and 19

(i) The LCM of 19 and 12 is associative

LCM of 12 and 19 = LCM of 19 and 12

Frequently Asked Questions on LCM of 12 and 19

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.