What is the Least Common Multiple of 76785 and 76800?

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 76785 and 76800 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 76785 and 76800, than apply into the LCM equation.

GCF(76785,76800) = 15
LCM(76785,76800) = ( 76785 × 76800) / 15
LCM(76785,76800) = 5897088000 / 15
LCM(76785,76800) = 393139200

Least Common Multiple (LCM) of 76785 and 76800 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76785 and 76800. First we will calculate the prime factors of 76785 and 76800.

Prime Factorization of 76785

Prime Factorization of 76800

Now multiplying the highest exponent prime factors to calculate the LCM of 76785 and 76800.

LCM(76785,76800) = 3¹ × 5² × 5119¹ × 2¹⁰
LCM(76785,76800) = 393139200