What is the Least Common Multiple of 78306 and 78312?

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 78306 and 78312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78306 and 78312, than apply into the LCM equation.

GCF(78306,78312) = 6
LCM(78306,78312) = ( 78306 × 78312) / 6
LCM(78306,78312) = 6132299472 / 6
LCM(78306,78312) = 1022049912

Least Common Multiple (LCM) of 78306 and 78312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78306 and 78312. First we will calculate the prime factors of 78306 and 78312.

Prime Factorization of 78306

Prime Factorization of 78312

Now multiplying the highest exponent prime factors to calculate the LCM of 78306 and 78312.

LCM(78306,78312) = 2³ × 3¹ × 31¹ × 421¹ × 13¹ × 251¹
LCM(78306,78312) = 1022049912