What is the Least Common Multiple of 45705 and 45723?

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 45705 and 45723 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45705 and 45723, than apply into the LCM equation.

GCF(45705,45723) = 3
LCM(45705,45723) = ( 45705 × 45723) / 3
LCM(45705,45723) = 2089769715 / 3
LCM(45705,45723) = 696589905

Least Common Multiple (LCM) of 45705 and 45723 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45705 and 45723. First we will calculate the prime factors of 45705 and 45723.

Prime Factorization of 45705

Prime Factorization of 45723

Now multiplying the highest exponent prime factors to calculate the LCM of 45705 and 45723.

LCM(45705,45723) = 3¹ × 5¹ × 11¹ × 277¹ × 15241¹
LCM(45705,45723) = 696589905