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What is the Least Common Multiple of 1987 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 (LCM) of 1987 and 2000 is 3974000.

LCM(1987,2000) = 3974000

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Least Common Multiple of 1987 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 1987 and 2000, than apply into the LCM equation.

GCF(1987,2000) = 1
LCM(1987,2000) = ( 1987 × 2000) / 1
LCM(1987,2000) = 3974000 / 1
LCM(1987,2000) = 3974000

Least Common Multiple (LCM) of 1987 and 2000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1987 and 2000. First we will calculate the prime factors of 1987 and 2000.

Prime Factorization of 1987

Prime factors of 1987 are 1987. Prime factorization of 1987 in exponential form is:

1987 = 19871

Prime Factorization of 2000

Prime factors of 2000 are 2, 5. Prime factorization of 2000 in exponential form is:

2000 = 24 × 53

Now multiplying the highest exponent prime factors to calculate the LCM of 1987 and 2000.

LCM(1987,2000) = 19871 × 24 × 53
LCM(1987,2000) = 3974000