What is the Least Common Multiple of 72306 and 72314?

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 72306 and 72314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72306 and 72314, than apply into the LCM equation.

GCF(72306,72314) = 2
LCM(72306,72314) = ( 72306 × 72314) / 2
LCM(72306,72314) = 5228736084 / 2
LCM(72306,72314) = 2614368042

Least Common Multiple (LCM) of 72306 and 72314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72306 and 72314. First we will calculate the prime factors of 72306 and 72314.

Prime Factorization of 72306

Prime Factorization of 72314

Now multiplying the highest exponent prime factors to calculate the LCM of 72306 and 72314.

LCM(72306,72314) = 2¹ × 3³ × 13¹ × 103¹ × 11¹ × 19¹ × 173¹
LCM(72306,72314) = 2614368042