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What is the Least Common Multiple of 1984 and 1994?

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 1984 and 1994 is 1978048.

LCM(1984,1994) = 1978048

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Least Common Multiple of 1984 and 1994 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1984 and 1994, than apply into the LCM equation.

GCF(1984,1994) = 2
LCM(1984,1994) = ( 1984 × 1994) / 2
LCM(1984,1994) = 3956096 / 2
LCM(1984,1994) = 1978048

Least Common Multiple (LCM) of 1984 and 1994 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1984 and 1994. First we will calculate the prime factors of 1984 and 1994.

Prime Factorization of 1984

Prime factors of 1984 are 2, 31. Prime factorization of 1984 in exponential form is:

1984 = 26 × 311

Prime Factorization of 1994

Prime factors of 1994 are 2, 997. Prime factorization of 1994 in exponential form is:

1994 = 21 × 9971

Now multiplying the highest exponent prime factors to calculate the LCM of 1984 and 1994.

LCM(1984,1994) = 26 × 311 × 9971
LCM(1984,1994) = 1978048