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What is the Least Common Multiple of 12 and 19?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 12 and 19 is 228.

LCM(12,19) = 228

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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

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

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

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