What is the Least Common Multiple of 39984 and 40004?

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 40004 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 40004, than apply into the LCM equation.

GCF(39984,40004) = 4
LCM(39984,40004) = ( 39984 × 40004) / 4
LCM(39984,40004) = 1599519936 / 4
LCM(39984,40004) = 399879984

Least Common Multiple (LCM) of 39984 and 40004 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39984 and 40004. First we will calculate the prime factors of 39984 and 40004.

Prime Factorization of 39984

Prime Factorization of 40004

Now multiplying the highest exponent prime factors to calculate the LCM of 39984 and 40004.

LCM(39984,40004) = 2⁴ × 3¹ × 7² × 17¹ × 73¹ × 137¹
LCM(39984,40004) = 399879984