What is the Least Common Multiple of 54306 and 54314?

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 54306 and 54314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54306 and 54314, than apply into the LCM equation.

GCF(54306,54314) = 2
LCM(54306,54314) = ( 54306 × 54314) / 2
LCM(54306,54314) = 2949576084 / 2
LCM(54306,54314) = 1474788042

Least Common Multiple (LCM) of 54306 and 54314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54306 and 54314. First we will calculate the prime factors of 54306 and 54314.

Prime Factorization of 54306

Prime Factorization of 54314

Now multiplying the highest exponent prime factors to calculate the LCM of 54306 and 54314.

LCM(54306,54314) = 2¹ × 3² × 7¹ × 431¹ × 13¹ × 2089¹
LCM(54306,54314) = 1474788042