What is the Least Common Multiple of 5745 and 5750?

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 5745 and 5750 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5745 and 5750, than apply into the LCM equation.

GCF(5745,5750) = 5
LCM(5745,5750) = ( 5745 × 5750) / 5
LCM(5745,5750) = 33033750 / 5
LCM(5745,5750) = 6606750

Least Common Multiple (LCM) of 5745 and 5750 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5745 and 5750. First we will calculate the prime factors of 5745 and 5750.

Prime Factorization of 5745

Prime Factorization of 5750

Now multiplying the highest exponent prime factors to calculate the LCM of 5745 and 5750.

LCM(5745,5750) = 3¹ × 5³ × 383¹ × 2¹ × 23¹
LCM(5745,5750) = 6606750