What is the Least Common Multiple of 39204 and 39214?

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 39204 and 39214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39204 and 39214, than apply into the LCM equation.

GCF(39204,39214) = 2
LCM(39204,39214) = ( 39204 × 39214) / 2
LCM(39204,39214) = 1537345656 / 2
LCM(39204,39214) = 768672828

Least Common Multiple (LCM) of 39204 and 39214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39204 and 39214. First we will calculate the prime factors of 39204 and 39214.

Prime Factorization of 39204

Prime Factorization of 39214

Now multiplying the highest exponent prime factors to calculate the LCM of 39204 and 39214.

LCM(39204,39214) = 2² × 3⁴ × 11² × 7¹ × 2801¹
LCM(39204,39214) = 768672828