What is the Least Common Multiple of 58296 and 58314?

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 58296 and 58314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 58296 and 58314, than apply into the LCM equation.

GCF(58296,58314) = 6
LCM(58296,58314) = ( 58296 × 58314) / 6
LCM(58296,58314) = 3399472944 / 6
LCM(58296,58314) = 566578824

Least Common Multiple (LCM) of 58296 and 58314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 58296 and 58314. First we will calculate the prime factors of 58296 and 58314.

Prime Factorization of 58296

Prime Factorization of 58314

Now multiplying the highest exponent prime factors to calculate the LCM of 58296 and 58314.

LCM(58296,58314) = 2³ × 3¹ × 7¹ × 347¹ × 9719¹
LCM(58296,58314) = 566578824