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What is the Least Common Multiple of 1990 and 2001?

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 (LCM) of 1990 and 2001 is 3981990.

LCM(1990,2001) = 3981990

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Least Common Multiple of 1990 and 2001 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 2001, than apply into the LCM equation.

GCF(1990,2001) = 1
LCM(1990,2001) = ( 1990 × 2001) / 1
LCM(1990,2001) = 3981990 / 1
LCM(1990,2001) = 3981990

Least Common Multiple (LCM) of 1990 and 2001 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1990 and 2001. First we will calculate the prime factors of 1990 and 2001.

Prime Factorization of 1990

Prime factors of 1990 are 2, 5, 199. Prime factorization of 1990 in exponential form is:

1990 = 21 × 51 × 1991

Prime Factorization of 2001

Prime factors of 2001 are 3, 23, 29. Prime factorization of 2001 in exponential form is:

2001 = 31 × 231 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 1990 and 2001.

LCM(1990,2001) = 21 × 51 × 1991 × 31 × 231 × 291
LCM(1990,2001) = 3981990