What is the Least Common Multiple of 19980 and 19990?

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 19980 and 19990 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19980 and 19990, than apply into the LCM equation.

GCF(19980,19990) = 10
LCM(19980,19990) = ( 19980 × 19990) / 10
LCM(19980,19990) = 399400200 / 10
LCM(19980,19990) = 39940020

Least Common Multiple (LCM) of 19980 and 19990 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19980 and 19990. First we will calculate the prime factors of 19980 and 19990.

Prime Factorization of 19980

Prime Factorization of 19990

Now multiplying the highest exponent prime factors to calculate the LCM of 19980 and 19990.

LCM(19980,19990) = 2² × 3³ × 5¹ × 37¹ × 1999¹
LCM(19980,19990) = 39940020