What is the Least Common Multiple of 85100 and 85114?

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 85100 and 85114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85100 and 85114, than apply into the LCM equation.

GCF(85100,85114) = 2
LCM(85100,85114) = ( 85100 × 85114) / 2
LCM(85100,85114) = 7243201400 / 2
LCM(85100,85114) = 3621600700

Least Common Multiple (LCM) of 85100 and 85114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85100 and 85114. First we will calculate the prime factors of 85100 and 85114.

Prime Factorization of 85100

Prime Factorization of 85114

Now multiplying the highest exponent prime factors to calculate the LCM of 85100 and 85114.

LCM(85100,85114) = 2² × 5² × 23¹ × 37¹ × 42557¹
LCM(85100,85114) = 3621600700