What is the Least Common Multiple of 1990 and 1999?

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 1990 and 1999 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1990 and 1999, than apply into the LCM equation.

GCF(1990,1999) = 1
LCM(1990,1999) = ( 1990 × 1999) / 1
LCM(1990,1999) = 3978010 / 1
LCM(1990,1999) = 3978010

Least Common Multiple (LCM) of 1990 and 1999 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1990 and 1999. First we will calculate the prime factors of 1990 and 1999.

Prime Factorization of 1990

Prime Factorization of 1999

Now multiplying the highest exponent prime factors to calculate the LCM of 1990 and 1999.

LCM(1990,1999) = 2¹ × 5¹ × 199¹ × 1999¹
LCM(1990,1999) = 3978010