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What is the Least Common Multiple of 1983 and 1997?

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 1983 and 1997 is 3960051.

LCM(1983,1997) = 3960051

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Least Common Multiple of 1983 and 1997 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1983 and 1997, than apply into the LCM equation.

GCF(1983,1997) = 1
LCM(1983,1997) = ( 1983 × 1997) / 1
LCM(1983,1997) = 3960051 / 1
LCM(1983,1997) = 3960051

Least Common Multiple (LCM) of 1983 and 1997 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1983 and 1997. First we will calculate the prime factors of 1983 and 1997.

Prime Factorization of 1983

Prime factors of 1983 are 3, 661. Prime factorization of 1983 in exponential form is:

1983 = 31 × 6611

Prime Factorization of 1997

Prime factors of 1997 are 1997. Prime factorization of 1997 in exponential form is:

1997 = 19971

Now multiplying the highest exponent prime factors to calculate the LCM of 1983 and 1997.

LCM(1983,1997) = 31 × 6611 × 19971
LCM(1983,1997) = 3960051