What is the Least Common Multiple of 28785 and 28800?

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 28785 and 28800 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 28785 and 28800, than apply into the LCM equation.

GCF(28785,28800) = 15
LCM(28785,28800) = ( 28785 × 28800) / 15
LCM(28785,28800) = 829008000 / 15
LCM(28785,28800) = 55267200

Least Common Multiple (LCM) of 28785 and 28800 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 28785 and 28800. First we will calculate the prime factors of 28785 and 28800.

Prime Factorization of 28785

Prime Factorization of 28800

Now multiplying the highest exponent prime factors to calculate the LCM of 28785 and 28800.

LCM(28785,28800) = 3² × 5² × 19¹ × 101¹ × 2⁷
LCM(28785,28800) = 55267200