What is the Least Common Multiple of 75700 and 75720?

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 75700 and 75720 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75700 and 75720, than apply into the LCM equation.

GCF(75700,75720) = 20
LCM(75700,75720) = ( 75700 × 75720) / 20
LCM(75700,75720) = 5732004000 / 20
LCM(75700,75720) = 286600200

Least Common Multiple (LCM) of 75700 and 75720 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75700 and 75720. First we will calculate the prime factors of 75700 and 75720.

Prime Factorization of 75700

Prime Factorization of 75720

Now multiplying the highest exponent prime factors to calculate the LCM of 75700 and 75720.

LCM(75700,75720) = 2³ × 5² × 757¹ × 3¹ × 631¹
LCM(75700,75720) = 286600200