What is the Least Common Multiple of 28560 and 28575?

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 28560 and 28575 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 28560 and 28575, than apply into the LCM equation.

GCF(28560,28575) = 15
LCM(28560,28575) = ( 28560 × 28575) / 15
LCM(28560,28575) = 816102000 / 15
LCM(28560,28575) = 54406800

Least Common Multiple (LCM) of 28560 and 28575 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 28560 and 28575. First we will calculate the prime factors of 28560 and 28575.

Prime Factorization of 28560

Prime Factorization of 28575

Now multiplying the highest exponent prime factors to calculate the LCM of 28560 and 28575.

LCM(28560,28575) = 2⁴ × 3² × 5² × 7¹ × 17¹ × 127¹
LCM(28560,28575) = 54406800