What is the Least Common Multiple of 19489 and 19500?

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 19489 and 19500 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19489 and 19500, than apply into the LCM equation.

GCF(19489,19500) = 1
LCM(19489,19500) = ( 19489 × 19500) / 1
LCM(19489,19500) = 380035500 / 1
LCM(19489,19500) = 380035500

Least Common Multiple (LCM) of 19489 and 19500 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19489 and 19500. First we will calculate the prime factors of 19489 and 19500.

Prime Factorization of 19489

Prime Factorization of 19500

Now multiplying the highest exponent prime factors to calculate the LCM of 19489 and 19500.

LCM(19489,19500) = 19489¹ × 2² × 3¹ × 5³ × 13¹
LCM(19489,19500) = 380035500