What is the Least Common Multiple of 78300 and 78314?

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 78300 and 78314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78300 and 78314, than apply into the LCM equation.

GCF(78300,78314) = 2
LCM(78300,78314) = ( 78300 × 78314) / 2
LCM(78300,78314) = 6131986200 / 2
LCM(78300,78314) = 3065993100

Least Common Multiple (LCM) of 78300 and 78314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78300 and 78314. First we will calculate the prime factors of 78300 and 78314.

Prime Factorization of 78300

Prime Factorization of 78314

Now multiplying the highest exponent prime factors to calculate the LCM of 78300 and 78314.

LCM(78300,78314) = 2² × 3³ × 5² × 29¹ × 39157¹
LCM(78300,78314) = 3065993100