What is the Least Common Multiple of 19000 and 19014?

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 of 19000 and 19014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19000 and 19014, than apply into the LCM equation.

GCF(19000,19014) = 2
LCM(19000,19014) = ( 19000 × 19014) / 2
LCM(19000,19014) = 361266000 / 2
LCM(19000,19014) = 180633000

Least Common Multiple (LCM) of 19000 and 19014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19000 and 19014. First we will calculate the prime factors of 19000 and 19014.

Prime Factorization of 19000

Prime Factorization of 19014

Now multiplying the highest exponent prime factors to calculate the LCM of 19000 and 19014.

LCM(19000,19014) = 2³ × 5³ × 19¹ × 3¹ × 3169¹
LCM(19000,19014) = 180633000