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What is the Least Common Multiple of 1981 and 1996?

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 1981 and 1996 is 3954076.

LCM(1981,1996) = 3954076

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Least Common Multiple of 1981 and 1996 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1981 and 1996, than apply into the LCM equation.

GCF(1981,1996) = 1
LCM(1981,1996) = ( 1981 × 1996) / 1
LCM(1981,1996) = 3954076 / 1
LCM(1981,1996) = 3954076

Least Common Multiple (LCM) of 1981 and 1996 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1981 and 1996. First we will calculate the prime factors of 1981 and 1996.

Prime Factorization of 1981

Prime factors of 1981 are 7, 283. Prime factorization of 1981 in exponential form is:

1981 = 71 × 2831

Prime Factorization of 1996

Prime factors of 1996 are 2, 499. Prime factorization of 1996 in exponential form is:

1996 = 22 × 4991

Now multiplying the highest exponent prime factors to calculate the LCM of 1981 and 1996.

LCM(1981,1996) = 71 × 2831 × 22 × 4991
LCM(1981,1996) = 3954076