What is the Least Common Multiple of 28305 and 28320?

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 28305 and 28320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 28305 and 28320, than apply into the LCM equation.

GCF(28305,28320) = 15
LCM(28305,28320) = ( 28305 × 28320) / 15
LCM(28305,28320) = 801597600 / 15
LCM(28305,28320) = 53439840

Least Common Multiple (LCM) of 28305 and 28320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 28305 and 28320. First we will calculate the prime factors of 28305 and 28320.

Prime Factorization of 28305

Prime Factorization of 28320

Now multiplying the highest exponent prime factors to calculate the LCM of 28305 and 28320.

LCM(28305,28320) = 3² × 5¹ × 17¹ × 37¹ × 2⁵ × 59¹
LCM(28305,28320) = 53439840