What is the Least Common Multiple of 39904 and 39924?

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 39904 and 39924 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39904 and 39924, than apply into the LCM equation.

GCF(39904,39924) = 4
LCM(39904,39924) = ( 39904 × 39924) / 4
LCM(39904,39924) = 1593127296 / 4
LCM(39904,39924) = 398281824

Least Common Multiple (LCM) of 39904 and 39924 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39904 and 39924. First we will calculate the prime factors of 39904 and 39924.

Prime Factorization of 39904

Prime Factorization of 39924

Now multiplying the highest exponent prime factors to calculate the LCM of 39904 and 39924.

LCM(39904,39924) = 2⁵ × 29¹ × 43¹ × 3² × 1109¹
LCM(39904,39924) = 398281824