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What is the Least Common Multiple of 19 and 38?

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 19 and 38 is 38.

LCM(19,38) = 38

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Least Common Multiple of 19 and 38 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19 and 38, than apply into the LCM equation.

GCF(19,38) = 19
LCM(19,38) = ( 19 × 38) / 19
LCM(19,38) = 722 / 19
LCM(19,38) = 38

Least Common Multiple (LCM) of 19 and 38 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19 and 38. First we will calculate the prime factors of 19 and 38.

Prime Factorization of 19

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

19 = 191

Prime Factorization of 38

Prime factors of 38 are 2, 19. Prime factorization of 38 in exponential form is:

38 = 21 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 19 and 38.

LCM(19,38) = 191 × 21
LCM(19,38) = 38

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