What is the Least Common Multiple of 75705 and 75723?

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 75705 and 75723 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75705 and 75723, than apply into the LCM equation.

GCF(75705,75723) = 3
LCM(75705,75723) = ( 75705 × 75723) / 3
LCM(75705,75723) = 5732609715 / 3
LCM(75705,75723) = 1910869905

Least Common Multiple (LCM) of 75705 and 75723 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75705 and 75723. First we will calculate the prime factors of 75705 and 75723.

Prime Factorization of 75705

Prime Factorization of 75723

Now multiplying the highest exponent prime factors to calculate the LCM of 75705 and 75723.

LCM(75705,75723) = 3¹ × 5¹ × 7² × 103¹ × 43¹ × 587¹
LCM(75705,75723) = 1910869905