What is the Least Common Multiple of 58305 and 58320?

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 58305 and 58320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 58305 and 58320, than apply into the LCM equation.

GCF(58305,58320) = 15
LCM(58305,58320) = ( 58305 × 58320) / 15
LCM(58305,58320) = 3400347600 / 15
LCM(58305,58320) = 226689840

Least Common Multiple (LCM) of 58305 and 58320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 58305 and 58320. First we will calculate the prime factors of 58305 and 58320.

Prime Factorization of 58305

Prime Factorization of 58320

Now multiplying the highest exponent prime factors to calculate the LCM of 58305 and 58320.

LCM(58305,58320) = 3⁶ × 5¹ × 13² × 23¹ × 2⁴
LCM(58305,58320) = 226689840