What is the Least Common Multiple of 85664 and 85680?

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 85664 and 85680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85664 and 85680, than apply into the LCM equation.

GCF(85664,85680) = 16
LCM(85664,85680) = ( 85664 × 85680) / 16
LCM(85664,85680) = 7339691520 / 16
LCM(85664,85680) = 458730720

Least Common Multiple (LCM) of 85664 and 85680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85664 and 85680. First we will calculate the prime factors of 85664 and 85680.

Prime Factorization of 85664

Prime Factorization of 85680

Now multiplying the highest exponent prime factors to calculate the LCM of 85664 and 85680.

LCM(85664,85680) = 2⁵ × 2677¹ × 3² × 5¹ × 7¹ × 17¹
LCM(85664,85680) = 458730720