What is the Least Common Multiple of 39984 and 39996?

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 39984 and 39996 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39984 and 39996, than apply into the LCM equation.

GCF(39984,39996) = 12
LCM(39984,39996) = ( 39984 × 39996) / 12
LCM(39984,39996) = 1599200064 / 12
LCM(39984,39996) = 133266672

Least Common Multiple (LCM) of 39984 and 39996 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39984 and 39996. First we will calculate the prime factors of 39984 and 39996.

Prime Factorization of 39984

Prime Factorization of 39996

Now multiplying the highest exponent prime factors to calculate the LCM of 39984 and 39996.

LCM(39984,39996) = 2⁴ × 3² × 7² × 17¹ × 11¹ × 101¹
LCM(39984,39996) = 133266672