What is the Least Common Multiple of 38208 and 38214?

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 38208 and 38214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38208 and 38214, than apply into the LCM equation.

GCF(38208,38214) = 6
LCM(38208,38214) = ( 38208 × 38214) / 6
LCM(38208,38214) = 1460080512 / 6
LCM(38208,38214) = 243346752

Least Common Multiple (LCM) of 38208 and 38214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38208 and 38214. First we will calculate the prime factors of 38208 and 38214.

Prime Factorization of 38208

Prime Factorization of 38214

Now multiplying the highest exponent prime factors to calculate the LCM of 38208 and 38214.

LCM(38208,38214) = 2⁶ × 3² × 199¹ × 11¹ × 193¹
LCM(38208,38214) = 243346752