What is the Least Common Multiple of 1990 and 2000?

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 2000 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 2000, than apply into the LCM equation.

GCF(1990,2000) = 10
LCM(1990,2000) = ( 1990 × 2000) / 10
LCM(1990,2000) = 3980000 / 10
LCM(1990,2000) = 398000

Least Common Multiple (LCM) of 1990 and 2000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1990 and 2000. First we will calculate the prime factors of 1990 and 2000.

Prime Factorization of 1990

Prime Factorization of 2000

Now multiplying the highest exponent prime factors to calculate the LCM of 1990 and 2000.

LCM(1990,2000) = 2⁴ × 5³ × 199¹
LCM(1990,2000) = 398000