What is the Least Common Multiple of 85680 and 85696?

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 85680 and 85696 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85680 and 85696, than apply into the LCM equation.

GCF(85680,85696) = 16
LCM(85680,85696) = ( 85680 × 85696) / 16
LCM(85680,85696) = 7342433280 / 16
LCM(85680,85696) = 458902080

Least Common Multiple (LCM) of 85680 and 85696 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85680 and 85696. First we will calculate the prime factors of 85680 and 85696.

Prime Factorization of 85680

Prime Factorization of 85696

Now multiplying the highest exponent prime factors to calculate the LCM of 85680 and 85696.

LCM(85680,85696) = 2⁶ × 3² × 5¹ × 7¹ × 17¹ × 13¹ × 103¹
LCM(85680,85696) = 458902080