What is the Least Common Multiple of 85710 and 85728?

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 85710 and 85728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85710 and 85728, than apply into the LCM equation.

GCF(85710,85728) = 6
LCM(85710,85728) = ( 85710 × 85728) / 6
LCM(85710,85728) = 7347746880 / 6
LCM(85710,85728) = 1224624480

Least Common Multiple (LCM) of 85710 and 85728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85710 and 85728. First we will calculate the prime factors of 85710 and 85728.

Prime Factorization of 85710

Prime Factorization of 85728

Now multiplying the highest exponent prime factors to calculate the LCM of 85710 and 85728.

LCM(85710,85728) = 2⁵ × 3¹ × 5¹ × 2857¹ × 19¹ × 47¹
LCM(85710,85728) = 1224624480