What is the Least Common Multiple of 1983 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 of 1983 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 1983 and 1996, than apply into the LCM equation.

GCF(1983,1996) = 1
LCM(1983,1996) = ( 1983 × 1996) / 1
LCM(1983,1996) = 3958068 / 1
LCM(1983,1996) = 3958068

Least Common Multiple (LCM) of 1983 and 1996 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1983 and 1996. First we will calculate the prime factors of 1983 and 1996.

Prime Factorization of 1983

Prime Factorization of 1996

Now multiplying the highest exponent prime factors to calculate the LCM of 1983 and 1996.

LCM(1983,1996) = 3¹ × 661¹ × 2² × 499¹
LCM(1983,1996) = 3958068