What is the Least Common Multiple of 19380 and 19400?

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 19380 and 19400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19380 and 19400, than apply into the LCM equation.

GCF(19380,19400) = 20
LCM(19380,19400) = ( 19380 × 19400) / 20
LCM(19380,19400) = 375972000 / 20
LCM(19380,19400) = 18798600

Least Common Multiple (LCM) of 19380 and 19400 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19380 and 19400. First we will calculate the prime factors of 19380 and 19400.

Prime Factorization of 19380

Prime Factorization of 19400

Now multiplying the highest exponent prime factors to calculate the LCM of 19380 and 19400.

LCM(19380,19400) = 2³ × 3¹ × 5² × 17¹ × 19¹ × 97¹
LCM(19380,19400) = 18798600