What is the Least Common Multiple of 88305 and 88320?

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 88305 and 88320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 88305 and 88320, than apply into the LCM equation.

GCF(88305,88320) = 15
LCM(88305,88320) = ( 88305 × 88320) / 15
LCM(88305,88320) = 7799097600 / 15
LCM(88305,88320) = 519939840

Least Common Multiple (LCM) of 88305 and 88320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 88305 and 88320. First we will calculate the prime factors of 88305 and 88320.

Prime Factorization of 88305

Prime Factorization of 88320

Now multiplying the highest exponent prime factors to calculate the LCM of 88305 and 88320.

LCM(88305,88320) = 3¹ × 5¹ × 7¹ × 29² × 2⁸ × 23¹
LCM(88305,88320) = 519939840